MAT2705-01/02 14F Take Home Test 3 Print Name (Last, First) _________________________________|__
Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use equal signs and arrows when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC, MathCad). You may use technology for row reductions, matrix inverses, plotting and root finding without showing intermediate steps. Print the requested 9 technology plots, labeling them and annotating them appropriately by hand and attach to the end of your test. All differential equations should be solved "by hand" unless otherwise specified.
1. The displacement LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== of an underdamped harmonic oscillator system satisfies
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIuRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZURj0=
Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjRGJ0Y5Rjk= , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjRGJ0Y5Rjk= , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzM3RidGOUY5 and the initial conditions 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 .
a) Express this DE in standard form with a unit coefficient of the second derivative term. What are the natural frequency LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjBGJ0YyRjIvJS9zdWJzY3JpcHRzaGlmdEdGOw== , natural decay time LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYkLUkjbWlHRiQ2JVEmJnRhdTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjUtRiw2JC1JI21uR0YkNiRRIjBGJ0Y1RjUvJS9zdWJzY3JpcHRzaGlmdEdGPQ== , the quality factor 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and the period LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPS1JI21vR0YkNi1RIj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZILyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlctRjs2JFEiMkYnRj4tRkM2LVEifkYnRj5GRkZJRktGTUZPRlFGUy9GVlEmMC4wZW1GJy9GWUZbby1GLzYlUScmIzk2MDtGJy9GM0ZIRj5GPg==/LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtSSNtbkdGJDYkUSIwRidGMkYyLyUvc3Vic2NyaXB0c2hpZnRHRjs= for this system? (Give both exact and numeric values to 3 decimal places.)
Consider the following driving force functions LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== :
b) 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. Find the general solution of the differential equation. What is the frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUYjNiQtRiw2JS1JI21pR0YkNiVRJyYjOTY5O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21uR0YkNiRRIjFGJ0Y5L0Y3USV0cnVlRicvRjpRJ2l0YWxpY0YnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGOS1GIzYkLUYzNiNRIUYnRjlGRkY5 , decay time LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYkLUkjbWlHRiQ2JVEmJnRhdTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjUtRiw2JC1JI21uR0YkNiRRIjFGJ0Y1RjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== and the period 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/LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtSSNtbkdGJDYkUSIxRidGMkYyLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= for this decaying sinusoidal solution? (Give both exact and numeric values to 3 decimal places.c) 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. Solve the above initial value problem for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHRj0tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXLUY7NiRRIjFGJ0Y+LUZDNi1RIixGJ0Y+RkYvRkpGNEZLRk1GT0ZRRlMvRlZRJjAuMGVtRicvRllRLDAuMzMzMzMzM2VtRictRi82I1EnYHZfXzBgRidGQkZaRj4=. Evaluate the two envelope functions for the exponentially decaying sinusoidal function and plot (#1) all three together for 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LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXJvd0dGJDYkLUkjbWlHRiQ2JVEmJnRhdTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjUtRiw2JC1JI21uR0YkNiRRIjFGJ0Y1RjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==, fully labeling the axes and three curves. [You should see a number of oscillations before convergence to the horizontal axis. How many do you see in the chosen window? Does this agree with your value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EnYFRfXzFgRictRiw2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn?]d) 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. For the initial system at rest at equilibrium, find the maximum displacement from equilibrium and the time at which it occurs numerically to 4 decimal places. Find the solution using Maple and find the first extremal point on the curve using technology. Plot (#2) your solution for 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, whereLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2I1ErYCZ0YXU7X19wYEYnRi8= is the characteristic time for the exponential factor here. Compare your coordinate values to your graph, annotating the maximal point on the graph.
e) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUZANi1RIn5GJ0Y9RkNGRkZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZGZW5GVy1JI21uR0YkNiRRIzQ1RidGPUZXLUY2NiQtRiM2LC1GaG42JFEiMkYnRj1GVy1GLDYlUSRjb3NGJy9GMEZFRj0tRjY2JC1GIzYmLUZobjYkUSIzRidGPUZXRjpGPUY9LUZANi1RKiZ1bWludXMwO0YnRj1GQ0ZGRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZhcEZqb0ZXLUYsNiVRJHNpbkYnRmVvRj1GZm9GPUY9Rj0=. Find the initial value problem solution for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHRj0tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXRjpGQi1GLzYjUSdgdl9fMGBGJ0Y+ by hand using matrix methods (but check with Maple!).f) Evaluate the values of the amplitude A and phase shift \316\264 for the steady state solution (the part of the solution which remains after the transient has died away). Evaluate the relative phase shift LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EvYCZkZWx0YTtfX3JlbGBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= by subtracting the phase shift LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX2RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn of the driving function. Express this relative phase shift in radians, degrees and cycles (divide radians by 2\317\200). What is the ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJBRidGL0YyRjk=/LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYEFfX2RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn of the response (steady state) amplitude to the driving force amplitude LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYEFfX2RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==? (amplification factor).
g) Make a single plot (#3) in an appropriate viewing window (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) showing both the solution function and the steady state solution until they merge. In a separate plot for comparison with the driving sine function, plot (#4) both the steady state solution and the driving function rescaled to have the same amplitude as the steady state solution in order to see how the peaks of the steady state solution compare to the peaks of the driving function, using the window 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 , where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYFRfX2RgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn is the period of the driving function. Does your plot agree with your calculated relative phase shift angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EvYCZkZWx0YTtfX3JlbGBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= (does the steady state solution lead ahead in time [peaks earlier] or lag behind in time [peaks later] the driving function by a corresponding amount)? Explain.h) 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 .Explore resonance for this system by finding the steady state solution by hand, where the frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy of the driving force function is a parameter. i) Evaluate the steady state amplitude function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY5O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj8tRiw2I1EhRidGPw== and its limit 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. Does your value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiM0YnL0YzUSdub3JtYWxGJ0Y+Rj5GPg== of the amplification factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY5O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj8tSSNtb0dGJDYtUSI9RidGPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtRiw2JVEiQUYnRi9GMkY1LUYsNiNRIUYnRj8=/ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiUtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJCRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYkUSIwRicvRjtRJ25vcm1hbEYnRkMvJS9zdWJzY3JpcHRzaGlmdEdGQi1JJW1zdXBHRiQ2JS1GNDYlUSgmb21lZ2E7RicvRjhRJmZhbHNlRidGQy1GIzYkLUZANiRRIjJGJ0ZDRkMvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZCRkNGQ0ZD agree with your value for part f) as it should?j) Use calculus to find the exact and numerical values of both the frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiM2JC1GLDYlUSgmb21lZ2E7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y6LUYjNiQtRiw2JVEicEYnL0Y4USV0cnVlRicvRjtRJ2l0YWxpY0YnRjovJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRjo= and the amplitude ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtSSVtc3ViR0YkNiUtRiw2JVEoJm9tZWdhO0YnL0Y1USZmYWxzZUYnL0Y4USdub3JtYWxGJy1GIzYkLUYsNiVRInBGJ0Y0RjdGRy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkdGR0ZHRitGRw==/ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRRj5GPkY+ where it has its peak value for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RLyZHcmVhdGVyRXF1YWw7RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUSIwRidGMkYy. What is the numerical value ofLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtSSVtc3ViR0YkNiUtRiw2JVEoJm9tZWdhO0YnL0Y1USZmYWxzZUYnL0Y4USdub3JtYWxGJy1GIzYkLUYsNiVRInBGJ0Y0RjdGRy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkdGR0ZHRitGRw==/ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRRj5GPkY+ and how does the its value compare to the quality factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ? k) Plot (#5) the amplitude function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEnJiM5Njk7RicvRjVRJmZhbHNlRicvRjhRJ25vcm1hbEYnRkRGREZERitGRA==/ 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 in an appropriate window (showing the limiting behavior of the entire function for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RLyZHcmVhdGVyRXF1YWw7RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUSIwRidGMkYy and hand annotate on your axes the values of 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 and corresponding amplitudes and indicate the points on the curve which correspond to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYlUSgmb21lZ2E7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUkjbW5HRiQ2JFEiMEYnRjpGOi8lL3N1YnNjcmlwdHNoaWZ0R0ZCRitGOkYrRjo= and LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtRiw2JVEicEYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==.2. 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,
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 ; 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 , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzIwRidGOUY5 , 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 .a) Write this closed 3 tank mixing tank system of differential equations for the vector variable 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 = 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 AND its initial conditions in explicit matrix form (showing all components, not just vector symbols) and identifying the coefficient matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.b) Use the eigenvector approach to find its general solution by hand, showing all steps.c) Find the IVP solution, using matrix methods showing all steps. Make sure it agrees with Maple's solution.d) Evaluate the asymptotic solution 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 for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZzcmFycjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSgmaW5maW47RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY5, which is the equilibrium solution approached by your solution.e) Plot (#6) the three solution curves together with their horizontal asymptotes in an appropriate viewing window (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RLyZHcmVhdGVyRXF1YWw7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSIwRidGOS1GNjYtUSIhRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjExMTExMTFlbUYnL0ZORldGOQ==) that shows them reaching and settling down to those equilibrium values without compressing the interesting part before reaching that limit. Label each curve. Comment about your choice of viewing window in relation to the characteristic decay time of the problem.3. 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.a) Identify the coefficient matrix and by hand find a new basis for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0Y+LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y+ consisting of eigenvectors 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 of this matrix using the standard hand recipe, rescaling them to be the minimal integer eigenvectors. Order the real eigenvalues 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 by decreasing value (increasing absolute value). Identify 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.b) Evaluate the new coordinates 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 of the point 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 with respect to this basis of eigenvectors.c) Solve this initial value problem by hand, showing all steps.d) Use technology to plot (#7) a directionfield for this DE with the solution curve through the single initial data point, and (by hand if necessary) include the lines through the two eigenvectors representing the two subspaces of eigenvectors. Choose an appropriate window that shows everything clearly without wasting additional window space. By hand label these lines by their new coordinate labels, draw in and label the eigenvectors and the initial data vector 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 themselves as arrows, and include the parallelogram projection of the latter vector onto the new coordinate axes, i.e., the parallelogram parallel to the new coordinate axes with the initial data vector as the main diagonal. Do the projections along the coordinate axes agree with the values you found for the new coordinates of this vector? Explain. Does your directionfield correspond to the eigenvectors you have drawn? Explain why.e) Plot (#8) the two variables versus LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=JSFH for an appropriate viewing window for this initial value problem. Explain your window choice.The function LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn has a global maximum (for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=) , obvious in a separate plot (#9) of this variable. Find its coordinates and the corresponding value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= exactly and approximately (Maple is helpful to evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiKEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EldHJ1ZUYnLyUqc2VwYXJhdG9yR1EmZmFsc2VGJy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZELUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR0Y0L0YwUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnRi9GLy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRi8=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiKUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EldHJ1ZUYnLyUqc2VwYXJhdG9yR1EmZmFsc2VGJy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZELUkobWZlbmNlZEdGJDYkLUYjNiQtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJ0RicvJSdpdGFsaWNHRjQvRjBRJ2l0YWxpY0YnLUYjNiUtRlA2JVEkbWF4RicvRlRGN0YvRlNGVS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRi9GL0Yv exactly). Annotate your diagram to show this point.Advice. When in doubt about how much work to show, show more. Explain using words if it helps. Think of this take-home test as an exercise in "writing intensive" technical expression. Try to impress bob as though it were material for a job interview. In a real world technical job, you need to be able to write coherent technical reports that other people can follow.solution1. damped harmonic 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no 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These come from the complex exponentials with rate coefficients given by the roots of this quadratic equation, obtained by substituting the trial exponential 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into the homogeneous DE.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The characteristic time is 2 so 5 characteristic times is 10, we go to ? to see the pixels at the peeks merge completely. We should see about the following number of oscillations in a decay window of width 5 characteristic 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Perhaps 4 decay times is more realistic: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 are comparable as they should be for this value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiLkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8=c)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)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZNLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GUy1JI21uR0YkNiRRIzM2RidGOUZPRk8tRiw2JVEidEYnRi9GMkZPLUklbXN1cEdGJDYlLUY2Ni1RLyZFeHBvbmVudGlhbEU7RidGOS9GPFEmdW5zZXRGJy9GP0Zdby9GQUZdby9GQ0Zdby9GRUZdby9GR0Zdby9GSUZdb0ZSL0ZOUSwwLjExMTExMTFlbUYnLUYjNiwtRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORlxwRk8tRlY2JFEiMkYnRjlGT0ZZRi8vJStmb3JlZ3JvdW5kR1ErWzAsMTYwLDgwXUYnLyUscGxhY2Vob2xkZXJHRjEvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjFGMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LVEiO0YnRjlGOy9GP0YxRkBGQkZERkZGSEZSRk1GTy1GLDYlUSZpbml0c0YnRi9GMkY1LUYsNiVRInhGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2JC1GVjYkRmpwRjlGOUY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRmpxLUY2Ni1RIixGJ0Y5RjtGXnFGQEZCRkRGRkZIRlIvRk5RLDAuMzMzMzMzM2VtRidGYnEtRjY2LVEiJ0YnRjlGO0Y+RkBGQkZERkZGSC9GS0Zlb0ZURmVxRlxyRmpxRltxLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlMvJSZkZXB0aEdGXXMvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictSSZtZnJhY0dGJDYoLUYsNiVRJGRlcUYnRi9GMi1GIzYkLUYsNiVRIm1GJ0YvRjJGOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZXQvJSliZXZlbGxlZEdGPUZbcUZoci1GaXI2JkZbc0Zec0Zgcy9GY3NRJWF1dG9GJy1GLDYlUSVzb2wzRidGL0YyLUY2Ni5GOEYvRjJGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEnZHNvbHZlRidGL0YyLUZmcTYkLUYjNictRmZxNiYtRiM2JkZocy1GNjYuRmFyRi9GMkY7Rl5xRkBGQkZERkZGSEZSRmJyRl9xRjlGOS8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGX3JGYnEtRmZxNiQtRiM2JEZZRjlGOUY5RjktRjY2LkZdcS8lK2V4ZWN1dGFibGVHRj1GOUY7Rl5xRkBGQkZERkZGSEZSRk1GaHItRiw2JlEmZXZhbGZGJ0YvRlx3RjItRmZxNiUtRiM2Ji1GLDYmUSIlRidGL0Zcd0YyLUY2Ni5GYXJGXHdGOUY7Rl5xRkBGQkZERkZGSEZSRmJyLUZWNiVRIjRGJ0Zcd0Y5RjlGXHdGOUZqdkZoci1GLDYmUSVwbG90RidGL0Zcd0YyLUZmcTYkLUYjNjotRiw2JVEkcmhzRidGL0YyLUZmcTYkLUYjNiRGXnVGOUY5Rl9yRllGXHJGanEtRjY2LVEjLi5GJ0Y5RjtGPkZARkJGREZGRkhGW3BGVC1GVjYkUSI1RidGOUZPLUYsNiVRJyYjOTY0O0YnL0YwRj1GOUZfckZPLUYsNiVRJmNvbG9yRidGL0YyRlxyLUYsNiVRJHJlZEYnRmR5RjlGX3ItRiw2JVEqdGhpY2tuZXNzRidGL0YyRlxyRl5wRl9yLUYsNiVRKmdyaWRsaW5lc0YnRi9GMkZcci1GLDYlRjFGL0YyRjlGOUZcd0Y5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkmbWZyYWNHRiQ2KC1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUYjNiZGLi1GLzYtUSJ+RidGMi9GNlEmZmFsc2VGJy9GOUZPL0Y7Rk8vRj1GTy9GP0ZPL0ZBRk8vRkNGT0ZERkctSSNtaUdGJDYlUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvRjNRJ2l0YWxpY0YnRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl5vLyUpYmV2ZWxsZWRHRk9GSy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUZXNiNRIUYnLUYjNi0tRi82LVEqJnVtaW51czA7RidGMkZORlBGUUZSRlNGVEZVL0ZFUSwwLjIyMjIyMjJlbUYnL0ZIRmFwLUYjNiotRiw2KC1JI21uR0YkNiRRIjRGJ0YyLUZocDYkUSMyNUYnRjJGaW5GXG9GX29GYW8tRi82LlExJkludmlzaWJsZVRpbWVzO0YnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRjJGTkZQRlFGUkZTRlRGVUZERkctRiM2Ki1JJW1zdXBHRiQ2JS1GLzYtUS8mRXhwb25lbnRpYWxFO0YnRjJGTkZQRlFGUkZTRlRGVUZEL0ZIUSwwLjExMTExMTFlbUYnLUYjNilGXXAtRiM2Ki1GLDYoLUZocDYkRltvRjItRmhwNiRRIjJGJ0YyRmluRlxvRl9vRmFvRl5xLUYjNihGVi8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lK2V4ZWN1dGFibGVHRk8vJSlyZWFkb25seUdGZm4vRmJxUSoyRH5PdXRwdXRGJ0YyRltzRl5zRmBzRmJzRjJGW3NGXnNGYHNGYnNGMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGXnEtRiM2Ki1GVzYlUSRzaW5GJy9GZW5GT0YyLUYvNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjJGTkZQRlFGUkZTRlRGVUZERkctRmRvNiQtRiM2KC1GIzYqLUZocDYkUSIzRidGMkZecUZWRltzRl5zRmBzRmJzRjJGW3NGXnNGYHNGYnNGMkYyRltzRl5zRmBzRmJzRjJGW3NGXnNGYHNGYnNGMkZbc0Zec0Zgc0Zic0YyLUYvNi1RKCZtaW51cztGJ0YyRk5GUEZRRlJGU0ZURlVGYHBGYnAtRiM2Ki1GLDYoLUZocDYkUSMxNkYnRjItRmhwNiRRIzc1RidGMkZpbkZcb0Zfb0Zhb0ZecS1GIzYqRmZxRl5xLUYjNiotRlc2JVEkY29zRidGXHRGMkZddEZgdEZbc0Zec0Zgc0Zic0YyRltzRl5zRmBzRmJzRjJGW3NGXnNGYHNGYnNGMi1GLzYtUSIrRidGMkZORlBGUUZSRlNGVEZVRmBwRmJwLUYjNiotRiw2KEZncEZjdUZpbkZcb0Zfb0Zhb0ZecS1GIzYqLUZkbzYkLUYjNiotRiM2Ki1GaHA2JFEjMTVGJ0YyRl5xRlZGW3NGXnNGYHNGYnNGMkZddkZncEZbc0Zec0Zgc0Zic0YyRjJGXnEtRmdxNiVGaXEtRiM2K0ZdcEZmckZLRlZGW3NGXnNGYHNGYnNGMkZkc0Zbc0Zec0Zgc0Zic0YyRltzRl5zRmBzRmJzRjJGW3NGXnNGYHNGYnNGMkZob0Zec0YyRjItRi82LVEiPUYnRjJGTkZQRlFGUkZTRlRGVS9GRVEsMC4yNzc3Nzc4ZW1GJy9GSEZndy1GaHA2JEZmc0YyLUYvNi1RIjtGJ0YyRk4vRjlGZm5GUUZSRlNGVEZVRkRGaHdGSy1GVzYlUSVUbWF4RidGWkZnbi1GLzYtUSomY29sb25lcTtGJ0YyRk5GUEZRRlJGU0ZURlVGZndGaHdGSy1GVzYlUSdmc29sdmVGJ0ZaRmduLUZkbzYkLUYjNistRlc2JVEiJUYnRlpGZ24tRi82LVEiLEYnRjJGTkZeeEZRRlJGU0ZURlVGRC9GSFEsMC4zMzMzMzMzZW1GJ0ZWRmN3Rml3LUYvNi1RIy4uRidGMkZORlBGUUZSRlNGVEZVRmBwRkdGZnJGXnNGMkYyRlt4RkstRlc2JVEoRGlzcG1heEYnRlpGZ25GYngtRlc2JVElZXZhbEYnRlpGZ24tRmRvNiQtRiM2PEZdcEZlcEZecUZmcUZecUZpc0ZgdEZpdEZedUZecUZmcUZecUZqdUZgdEZddkZidkZecUZmdkZecUZfd0ZfeUZWRmN3Rl94Rl5zRjJGMkZec0Yye)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 difference from 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The response is about 85 degrees behind in time of the driving function curve, just short of a quarter cycle behind (to the right of) that driving function. Here is a 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Now we plot the steady state solution (blue) and a rescaled driving function (green) to compare the phase 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The blue steady state curve is indeed about 1/4 cycle behind the green driving function curve in time (to the right).Method of undetermined coefficients: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matrix form of solution: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oscillating 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form of solution: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This reduces to the correct result for frequency 3 if we 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoaWZhY3RvckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUkjbW5HRiQ2JFElMTM2OUYnL0YzUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj5GPkZARj4=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpc2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSpBbXBsaXR1ZGVGJ0YvRjItRjY2JC1GIzYlLUYsNiVRIldGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGR0ZERkdGR0ZERkc=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197136/1225 );evalf[5]( 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ElZ3JheUYnRk9GUkZfcUZjc0Y1RjVGaXBGXHFGX3EtRiw2JVEqZ3JpZGxpbmVzRidGT0ZSRmVxLUYsNiVGUUZPRlJGNUY1RjVGKy8lK2V4ZWN1dGFibGVHRjpGNQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjQjBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1GIzYkLUkjbWlHRiQ2JVEqQW1wbGl0dWRlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRjE2JVEid0YnRjRGNy9GOFEnbm9ybWFsRictRiM2JS1JI21uR0YkNiRRJC4yNUYnRkItSSNtb0dGJDYtUSJ+RidGQi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGUC8lKXN0cmV0Y2h5R0ZQLyUqc3ltbWV0cmljR0ZQLyUobGFyZ2VvcEdGUC8lLm1vdmFibGVsaW1pdHNHRlAvJSdhY2NlbnRHRlAvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zpbi1GMTYlUSNCMEYnRjRGNy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZG8vJSliZXZlbGxlZEdGUC1GSzYtUSI7RidGQkZOL0ZSRjZGU0ZVRldGWUZlbkZnbi9GW29RLDAuMjc3Nzc3OGVtRidGSi1GMTYlUSlzaW1wbGlmeUYnRjRGNy1GOzYkLUYjNiYtRiw2KC1GIzYjLUZHNiRRIjRGJ0ZCLUYjNiNGXG9GX29GYm9GZW9GZ29GSkYwLUY7NiQtRiM2Iy1JJW1zdWJHRiQ2JS1GMTYlUSgmb21lZ2E7RicvRjVGUEZCLUYjNiMtRkc2JFEiMEYnRkIvJS9zdWJzY3JpcHRzaGlmdEdGXnJGQkZCLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GNjYmLUYjNiUtRiw2JVEiV0YnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSVtc3ViR0YkNiUtRiw2JVEoJm9tZWdhO0YnL0YwRklGRS1GIzYjLUkjbW5HRiQ2JFEiMEYnRkUvJS9zdWJzY3JpcHRzaGlmdEdGYm9GRS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZFLUZCNi1RIjtGJ0ZFRkdGSkZMRk5GUEZSRlRGVi9GWlEsMC4yNzc3Nzc4ZW1GJy1GQjYtUSJ+RidGRUZHL0ZLRklGTEZORlBGUkZURlYvRlpGWEYrLUY2NiQtRiM2JEZgcC1GNjYmLUYjNistSSZtZnJhY0dGJDYoLUYjNiMtRmBvNiRRIjRGJ0ZFLUYjNiMtRiw2JVEjQjBGJ0YvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9yLyUpYmV2ZWxsZWRHRklGYHAtRiw2JVEqQW1wbGl0dWRlRidGL0YyLUY2NiQtRiM2I0Y+RkVGQUZdcUZgcEZkci1GNjYkLUYjNiNGZm5GRUZFRmVvRmhvRkU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiYtRiM2KS1GMDYmLUYjNiYtRiw2JVEiV0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GP1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSNtbkdGJDYkUSIwRidGRUZFRkUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGQS1GMDYmLUYjNiZGOEZBLUkmbWZyYWNHRiQ2KC1GIzYlLUYsNiVRKkFtcGxpdHVkZUYnRjtGPi1GMDYkLUYjNiRGOEZFRkVGRS1GIzYnLUZlbzYoLUZnbjYkUSIxRidGRS1GIzYlLUZnbjYkUSI0RidGRUY7Rj4vJS5saW5ldGhpY2tuZXNzR0ZmcC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZgcS8lKWJldmVsbGVkR0ZJLUZCNi1RIn5GJ0ZFRkcvRktGSUZMRk5GUEZSRlRGVi9GWkZYLUYsNiVRI0IwRidGO0Y+RjtGPkZccUZecUZhcUZjcUZFRkVGam5GXW9GQS1GIzYlRistRjA2Ji1GIzYmRmZuRkEtRmVvNihGZ28tRiM2Ji1GZW82KEZkcC1GIzYkRmlwRkVGXHFGXnFGYXFGY3FGZXFGanFGRUZccUZecUZhcUZjcUZFRkVGam5GXW9GRUYrRkVGRUZqbkZdb0ZBLUYwNiYtRiM2KC1GMDYmLUYjNiYtSSVtc3ViR0YkNiUtRiw2JVEoJm9tZWdhO0YnL0Y8RklGRS1GIzYkRmZuRkUvJS9zdWJzY3JpcHRzaGlmdEdGaW5GQUZmbkZFRkVGam5GXW9GQS1GMDYmLUYjNiZGY3NGQS1GZW82KC1GIzYlRmlvLUYwNiQtRiM2JUZjc0YrRkVGRUZFLUYjNidGZ3JGZXFGanFGO0Y+RlxxRl5xRmFxRmNxRkVGRUZqbkZdb0ZBLUYwNiYtRiM2JkZmbkZBRmJ0RkVGRUZqbkZdb0ZFRkVGam5GXW8vJStleGVjdXRhYmxlR0ZJRkU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUYsNiVRJXBsb3RGJ0YvRjItRjY2JC1GIzYtLUY2NiYtRiM2Ji1GNjYmLUYjNiYtRiw2JVEiV0YnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGVC8lKnN5bW1ldHJpY0dGVC8lKGxhcmdlb3BHRlQvJS5tb3ZhYmxlbGltaXRzR0ZULyUnYWNjZW50R0ZULyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSNtbkdGJDYkUSIwRidGUEZQRlAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGTC1GNjYmLUYjNiZGSUZMLUkmbWZyYWNHRiQ2KC1GIzYlLUYsNiVRKkFtcGxpdHVkZUYnRi9GMi1GNjYkLUYjNiRGSUZQRlBGUC1GIzYmLUZgcDYoLUZibzYkUSIxRidGUC1GIzYkLUZibzYkUSI0RidGUEZQLyUubGluZXRoaWNrbmVzc0dGYXEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGW3IvJSliZXZlbGxlZEdGVC1GTTYtUSJ+RidGUEZSL0ZWRlRGV0ZZRmVuRmduRmluRltvL0Zfb0Zdby1GLDYlUSNGMEYnRi9GMkZQRmdxRmlxRlxyRl5yRlBGUEZlb0Zob0ZQRlBGZW9GaG9GTC1GLDYlUSZjb2xvckYnRi9GMi1GTTYtUSI9RidGUEZSRmNyRldGWUZlbkZnbkZpbi9GXG9RLDAuMjc3Nzc3OGVtRicvRl9vRl9zLUYsNiVRJWJsdWVGJ0YvRjJGTC1GLDYlUSp0aGlja25lc3NGJ0YvRjJGW3NGX3EvJStleGVjdXRhYmxlR0ZURlBGUEZMRjotRjY2JC1GIzYtLUY2NiYtRiM2KS1GNjYmLUYjNiYtSSVtc3ViR0YkNiUtRiw2JVEoJm9tZWdhO0YnL0YwRlRGUC1GIzYkRmFvRlAvJS9zdWJzY3JpcHRzaGlmdEdGZG9GTEZhb0ZQRlBGZW9GaG9GTC1GNjYmLUYjNiZGZXRGTC1GYHA2KC1GIzYlRmRwLUY2NiQtRiM2JUZldC1GLDYjUSFGJ0ZQRlBGUEZbcUZncUZpcUZcckZeckZQRlBGZW9GaG9GTC1GNjYmLUYjNiZGYW9GTEZkdUZQRlBGZW9GaG9GZ3NGUEZQRmVvRmhvRkxGaHJGW3MtRiw2JVEmZ3JlZW5GJ0YvRjJGTEZkc0Zbc0ZfcUZnc0ZQRlBGZ3NGUEZQLUZNNi1RIjpGJ0ZQRlJGY3JGV0ZZRmVuRmduRmluRl5zRmBzRmByLUYsNiVRJnZlcnRzRidGL0YyLUZNNi1RKiZjb2xvbmVxO0YnRlBGUkZjckZXRllGZW5GZ25GaW5GXnNGYHMtRiw2JVEiJUYnRi9GMkZmdkZgckYrLUY2NiQtRiM2JUZpdkZnc0ZQRlBGZ3NGUA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY4LUY2NiYtRiM2Jy1JJm1mcmFjR0YkNigtRiM2Ji1GLDYlUSpBbXBsaXR1ZGVGJ0YvRjItRjY2JC1GIzYlLUYsNiVRIldGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGUEZNRlAtRiM2Jy1GPzYoLUkjbW5HRiQ2JFEiMUYnRlAtRiM2JS1GVzYkUSI0RidGUEYvRjIvJS5saW5ldGhpY2tuZXNzR0ZZLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl1vLyUpYmV2ZWxsZWRHRk8tSSNtb0dGJDYtUSJ+RidGUC8lJmZlbmNlR0ZPLyUqc2VwYXJhdG9yR0ZPLyUpc3RyZXRjaHlHRk8vJSpzeW1tZXRyaWNHRk8vJShsYXJnZW9wR0ZPLyUubW92YWJsZWxpbWl0c0dGTy8lJ2FjY2VudEdGTy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmZwLUYsNiVRI0YwRidGL0YyRi9GMkZpbkZbb0Zeb0Zgby1GY282LVEiLEYnRlBGZm8vRmlvRjFGam9GXHBGXnBGYHBGYnBGZHAvRmhwUSwwLjMzMzMzMzNlbUYnLUY/NigtRiM2JkZDLUY2NiQtRiM2Ji1GLDYjUSFGJy1GLDYlUSgmb21lZ2E7RicvRjBGT0ZQRk1GUEZQRk1GUEZSRmluRltvRl5vRmBvRk1GUEZQLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRlxxLUYsNiVRJyYjOTY5O0YnRmByRlAtRmNvNi1RIj1GJ0ZQRmZvRmhvRmpvRlxwRl5wRmBwRmJwL0ZlcFEsMC4yNzc3Nzc4ZW1GJy9GaHBGXnMtRlc2JFEiMEYnRlAtRmNvNi1RIy4uRidGUEZmb0Zob0Zqb0ZccEZecEZgcEZicC9GZXBRLDAuMjIyMjIyMmVtRidGZ3AtRlc2JFEjMzBGJ0ZQRlxxRmJvLUYsNiVRJmNvbG9yRidGL0YyRmpyLUY2NiYtRiM2Jy1GLDYlUSVjeWFuRidGL0YyRlxxLUYsNiVRJHJlZEYnRi9GMkZNRlBGUEZhckZkckZccS1GLDYlUSp0aGlja25lc3NGJ0YvRjJGanItRlc2JFEiMkYnRlBGXHEtRiw2JVEqZ3JpZGxpbmVzRidGL0YyRmpyLUYsNiVGMUYvRjJGTUZQRlAtRmNvNi1RIjtGJ0ZQRmZvRl9xRmpvRlxwRl5wRmBwRmJwRmRwRl9zRmJvLUYsNiVRKGRpc3BsYXlGJ0YvRjItRjY2JC1GIzYnLUYsNiVRIiVGJ0YvRjJGXHEtRiw2JVEmdmVydHNGJ0YvRjJGTUZQRlBGTUZQLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZA2. complex eigenvalue DE 3 tank mixing 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HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zqby8lKWJldmVsbGVkR0ZQLUYvNi1RIn5GJ0YyRk9GUUZSRlNGVEZVRlZGRC9GSEZGLUkjbWlHRiQ2JVEidEYnRmBvRmNvRmBvLyUrZm9yZWdyb3VuZEdRK1swLDE2MCw4MF1GJy8lLHBsYWNlaG9sZGVyR0Ziby8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGYm9GY28vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRl9wLUkobWZlbmNlZEdGJDYkLUYjNistRmRwNiVRJGNvc0YnL0Zhb0ZQRjItRmJxNiQtRiM2JS1GZW42KC1GIzYnRmduRl9wRmNwLyUrZXhlY3V0YWJsZUdGUEYyLUYjNiUtRmhuNiRRIzEwRidGMkZgb0Zjb0Zlb0Zob0ZbcEZdcEZickYyRjItRi82LVEiK0YnRjJGT0ZRRlJGU0ZURlVGVkZXRlktRmRwNiVRIklGJ0Zgb0Zjb0ZfcC1GZHA2JVEkc2luRidGaXFGMi1GYnE2JC1GIzYlLUZlbjYoLUYjNiZGZ25GX3BGY3BGMi1GIzYkRmZyRjJGZW9GaG9GW3BGXXBGYnJGMkYyRmJyRjJGMkZfcC1GYnE2KC1GIzYoLUknbXRhYmxlR0YkNjctSSRtdHJHRiQ2Ji1JJG10ZEdGJDYoLUYjNitGTC1GZW42KC1GaG42JFEiNEYnRjJGXW9GZW9GaG9GW3BGXXAtRi82LVEoJm1pbnVzO0YnRjJGT0ZRRlJGU0ZURlVGVkZXRlktRiM2Ki1GZW42KEZnbkZdb0Zlb0Zob0ZbcEZdcC1GLzYuUTEmSW52aXNpYmxlVGltZXM7RicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGMkZPRlFGUkZTRlRGVUZWRkRGYnAtRiM2KC1GaG42JEZec0YyL0ZocFEqWzAsMCwyNTVdRidGYnIvJSlyZWFkb25seUdGYm8vRlt2USoyRH5PdXRwdXRGJ0YyRmF2RmJyRmN2RmV2RjJGYXZGYnJGY3ZGZXZGMi8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGaXYvJStncm91cGFsaWduR0Zpdi8lKHJvd3NwYW5HRmdvLyUrY29sdW1uc3BhbkdGZ29GZ3ZGanZGXHctRmR0NiYtRmd0NigtRiM2K0ZMLUZlbjYoLUZobjYkRmdvRjJGXW9GZW9GaG9GW3BGXXBGaXJGY3VGYXZGYnJGY3ZGZXZGMkZndkZqdkZcd0Zed0Zgd0ZndkZqdkZcdy1GZHQ2Ji1GZ3Q2KEZqd0ZndkZqdkZcd0Zed0Zgd0ZndkZqdkZcdy8lJmFsaWduR1ElYXhpc0YnL0ZodlEpYmFzZWxpbmVGJy9GW3dGam8vRl13USd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGYm8vJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0ZceS8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0ZneS8lJmZyYW1lR0ZneS8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRlAvJS1lcXVhbGNvbHVtbnNHRlAvJS1kaXNwbGF5c3R5bGVHRlAvJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGZHlGYXZGYnJGY3ZGZXZGMkYyL0krbXNlbWFudGljc0dGJFEqQ29sVmVjdG9yRicvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGanotRi82LVEiO0YnRjJGTy9GOUZib0ZSRlNGVEZVRlZGRC9GSFEsMC4yNzc3Nzc4ZW1GJ0ZfcC1GZHA2JVEkbWFwRidGYG9GY28tRmJxNiQtRiM2Jy1GZHA2JVEmZXZhbGNGJ0Zgb0Zjby1GLzYtUSIsRidGMkZPRmZbbEZSRlNGVEZVRlZGRC9GSFEsMC4zMzMzMzMzZW1GJy1GZHA2JVEiJUYnRmBvRmNvRmJyRjJGMkZjW2xGX3AtRmRwNiVRI1gxRidGYG9GY28tRi82LVEqJmNvbG9uZXE7RidGMkZPRlFGUkZTRlRGVUZWL0ZFRmhbbEZnW2wtRmRwNiVRJXN1YnNGJ0Zgb0Zjby1GYnE2JC1GIzYpRlxzLUYvNi1RIj1GJ0YyRk9GUUZSRlNGVEZVRlZGYV1sRmdbbC1GaG42JEZgcUYyRmNcbEZoXGxGYnJGMkYyRmNbbEZfcC1GZHA2JVEjWDJGJ0Zgb0Zjb0ZeXWxGTEZcc0ZfcC1GYnE2JC1GIzYnLUZkcDYlUSMlJUYnRmBvRmNvRmB1RltdbEZickYyRjJGYnJGMg==JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY+LUkjbWlHRiQ2JVErc29sZ2VuaGFuZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYmLUYjNiotSSVtc3ViR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYlLUkjbW5HRiQ2JFEiMUYnRjlGL0YyLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GVTYlRlctRiM2JS1GZ242JFEiMkYnRjlGL0YyRmpuRl1vLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGYW8vRk5GYm8tRlU2JUZXLUYjNiUtRmduNiRRIjNGJ0Y5Ri9GMkZqbi8lK2V4ZWN1dGFibGVHRj1GOUY5LyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0ZccC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUZccC1GLDYlUSNjMUYnRi9GMkZccC1GLDYlUSdDb2x1bW5GJ0YvRjItRlA2JC1GIzYnLUYsNiVRIkJGJy9GMEY9RjlGXW9GZm5GZ3BGOUY5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZHItRiw2JVEjYzJGJ0YvRjJGXHAtRiw2JVEjWDFGJ0YvRjJGYHItRiw2JVEjYzNGJ0YvRjJGXHAtRiw2JVEjWDJGJ0YvRjItRjY2LVEiO0YnRjlGO0Zgb0ZARkJGREZGRkhGYW9GTUZccC1GLDYlUSVlcW5zRidGL0YyRjUtRiw2JVElc3Vic0YnRi9GMi1GUDYkLUYjNiotRiw2JVEidEYnRi9GMkZfcS1GZ242JEZcb0Y5Rl1vLUYsNiVRJHJoc0YnRi9GMi1GUDYkLUYjNiUtRiw2JVEiJUYnRi9GMkZncEY5RjlGZ3BGOUY5Rl9xLUZQNiYtRiM2KS1GZ242JFEiOUYnRjlGXW9GYnRGXW9GYnVGZ3BGOUY5RmlwRlxxRmdwRjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkobWFjdGlvbkdGJDYkLUkobWZlbmNlZEdGJDYoLUYjNiYtSSNtaUdGJDYjUSFGJy1JJ210YWJsZUdGJDY3LUkkbXRyR0YkNigtSSRtdGRHRiQ2KC1GIzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1GSTYkUSIyRidGTC8lJ2l0YWxpY0dRJXRydWVGJy9GTVEnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhuLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRkwvJSlyb3dhbGlnbkdGOS8lLGNvbHVtbmFsaWduR0Y5LyUrZ3JvdXBhbGlnbkdGOS8lKHJvd3NwYW5HRmVuLyUrY29sdW1uc3BhbkdGZW4tRkE2KC1GIzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RidGTC8lJmZlbmNlR0Zdby8lKnNlcGFyYXRvckdGXW8vJSlzdHJldGNoeUdGXW8vJSpzeW1tZXRyaWNHRl1vLyUobGFyZ2VvcEdGXW8vJS5tb3ZhYmxlbGltaXRzR0Zdby8lJ2FjY2VudEdGXW8vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZgcS1GRjYoLUZJNiRRIjRGJ0ZMLUYjNiVGSEZURldGWUZmbkZpbkZbb0ZMRl5vRmBvRmJvRmRvRmZvLUZBNigtRiM2JUZccC1GRjYoLUZJNiRRIjNGJ0ZMRmhxRllGZm5GaW5GW29GTEZeb0Zgb0Zib0Zkb0Zmb0Zeb0Zgb0Ziby1GPjYoLUZBNigtRiM2JC1GSTYkRmVuRkxGTEZeb0Zgb0Zib0Zkb0Zmby1GQTYoLUYjNiVGXHAtRkY2KEZpci1GIzYkRkhGTEZZRmZuRmluRltvRkxGXm9GYG9GYm9GZG9GZm8tRkE2KC1GIzYkRl5yRkxGXm9GYG9GYm9GZG9GZm9GXm9GYG9GYm8tRj42KEZlckZlci1GQTYoLUYjNiQtRkk2JFEiMEYnRkxGTEZeb0Zgb0Zib0Zkb0Zmb0Zeb0Zgb0Ziby8lJmFsaWduR1ElYXhpc0YnL0Zfb1EpYmFzZWxpbmVGJy9GYW9GaG4vRmNvUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGVi8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRlx1LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmd1LyUmZnJhbWVHRmd1LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGXW8vJS1lcXVhbGNvbHVtbnNHRl1vLyUtZGlzcGxheXN0eWxlR0Zdby8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZkdUY2RkxGTC9JK21zZW1hbnRpY3NHRiRRJ01hdHJpeEYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmp2LyUrYWN0aW9udHlwZUdRLnJ0YWJsZWFkZHJlc3NGJy1GIzYlRlxwRmlyRkwvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZfdEY2LyUrZXhlY3V0YWJsZUdGXW9GTA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkobWZlbmNlZEdGJDYmLUYjNiktSSNtaUdGJDYlUSNjMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEjYzJGJ0Y0RjdGOi1GMTYlUSNjM0YnRjRGNy8lK2V4ZWN1dGFibGVHRkJGPkY+LyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJy1GOzYtUSJ+RidGPkZAL0ZERkJGRUZHRklGS0ZNRk8vRlNGUS1GOzYtUSI9RidGPkZARmBvRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0Zmb0Zdby1JJW1zdXBHRiQ2JS1JKG1hY3Rpb25HRiQ2JC1GLDYoLUYjNiYtRjE2I1EhRictSSdtdGFibGVHRiQ2Ny1JJG10ckdGJDYoLUkkbXRkR0YkNigtRiM2JC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSI1RidGPi1GIzYkLUZkcTYkUSIyRidGPkY+LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zhci8lKWJldmVsbGVkR0ZCRj4vJSlyb3dhbGlnbkdGZHAvJSxjb2x1bW5hbGlnbkdGZHAvJStncm91cGFsaWduR0ZkcC8lKHJvd3NwYW5HRl5yLyUrY29sdW1uc3BhbkdGXnItRlxxNigtRiM2JS1GOzYtUSomdW1pbnVzMDtGJ0Y+RkBGYG9GRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRmhzLUZhcTYoLUZkcTYkUSI0RidGPi1GIzYkRmNxRj5GXHJGX3JGYnJGZHJGPkZmckZockZqckZcc0Zecy1GXHE2KC1GIzYlRmRzLUZhcTYoLUZkcTYkUSIzRidGPkZfdEZcckZfckZickZkckY+RmZyRmhyRmpyRlxzRl5zRmZyRmhyRmpyLUZpcDYoLUZccTYoLUYjNiQtRmRxNiRGXnJGPkY+RmZyRmhyRmpyRlxzRl5zLUZccTYoLUYjNiVGZHMtRmFxNihGYHVGX3RGXHJGX3JGYnJGZHJGPkZmckZockZqckZcc0Zecy1GXHE2KC1GIzYkRmV0Rj5GZnJGaHJGanJGXHNGXnNGZnJGaHJGanItRmlwNihGXHVGXHUtRlxxNigtRiM2JC1GZHE2JFEiMEYnRj5GPkZmckZockZqckZcc0Zec0ZmckZockZqci8lJmFsaWduR1ElYXhpc0YnL0ZnclEpYmFzZWxpbmVGJy9GaXJGYXIvRltzUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGNi8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmF3LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRlx4LyUmZnJhbWVHRlx4LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGQi8lLWVxdWFsY29sdW1uc0dGQi8lLWRpc3BsYXlzdHlsZUdGQi8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zpd0ZicEY+Rj4vSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy9GaG5RIltGJy9GW29RIl1GJ0ZfeS8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRictRiM2JUZkc0ZgdUY+LyUxc3VwZXJzY3JpcHRzaGlmdEdGZHZGXW8tRiw2KC1GIzYoLUZmcDY3LUZpcDYmLUZccTYoLUYjNiQtRmRxNiRRIjlGJ0Y+Rj5GZnJGaHJGanJGXHNGXnNGZnJGaHJGanItRmlwNiZGXnZGZnJGaHJGanItRmlwNiYtRlxxNigtRiM2JUZpekY0RjdGZnJGaHJGanJGXHNGXnNGZnJGaHJGanJGZXZGaHYvRmlyRlx5Rlt3Rl13Rl93RmJ3RmR3Rmd3Rmp3Rl14Rl94RmF4RmR4RmZ4Rmh4Rmp4Rl15LyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYnRmVuLyUpcmVhZG9ubHlHRjYvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0Y+Rj4vRmB5USpDb2xWZWN0b3JGJ0ZieUZkeUZdXGxGZW5GPg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkobWZlbmNlZEdGJDYmLUYjNiwtSSNtaUdGJDYlUSVzdWJzRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUZHNiQtRiM2NC1GTDYlUSNjMUYnRk9GUi1GLDYtUSI9RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjI3Nzc3NzhlbUYnL0ZFRmluLUkjbW5HRiQ2JFEiNEYnRi8tRiw2LVEiLEYnRi9GMi9GNkZRRjdGOUY7Rj1GP0ZBL0ZFUSwwLjMzMzMzMzNlbUYnLUZMNiVRI2MyRidGT0ZSRmVuLUZcbzYkUSI1RidGL0Zfby1GTDYlUSNjM0YnRk9GUkZlbi1GLDYtUSomdW1pbnVzMDtGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjIyMjIyMmVtRicvRkVGYnBGaG9GX28tRkw2JVEkcmhzRidGT0ZSLUZHNiQtRiM2JS1GTDYlUStzb2xnZW5oYW5kRidGT0ZSLyUrZXhlY3V0YWJsZUdGNEYvRi8tRkc2Ji1GIzYlLUZcbzYkUSIxRidGL0ZecUYvRi8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGXnFGL0YvRl9vRkstRkc2JC1GIzYzRlhGZW5GW29GX29GZW9GZW5GaG9GX29GW3BGZW5GXnBGaG9GX29GZHAtRkc2JC1GIzYkRltxRi9GLy1GRzYmLUYjNiQtRlxvNiRRIjJGJ0YvRi9GL0ZncUZqcUYvRi9GX29GSy1GRzYkLUYjNjNGWEZlbkZbb0Zfb0Zlb0ZlbkZob0Zfb0ZbcEZlbkZecEZob0Zfb0ZkcEZhci1GRzYmLUYjNiQtRlxvNiRRIjNGJ0YvRi9GL0ZncUZqcUYvRi9GXnFGL0YvL0ZocVEnJmxhbmc7RicvRltyUScmcmFuZztGJy1GLDYtUSI7RidGL0YyRmJvRjdGOUY7Rj1GP0ZBRmpuRistRkw2JVErc29saXZwaGFuZEYnRk9GUi1GLDYtUSomY29sb25lcTtGJ0YvRjJGNUY3RjlGO0Y9Rj9GaG5Gam4tRkw2JVEpc2ltcGxpZnlGJ0ZPRlItRkc2JC1GIzYlLUZMNiVRIiVGJ0ZPRlJGXnFGL0YvRl5xRi8=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=First we find the general solution and the IVP solution and plot the 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnc29saXZwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkwtRiw2JVErc29saXZwaGFuZEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJ3NvbGl2cEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOQ==JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=plot 5: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3. DE eigenbasis, 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adapting the coordinates to the eigenvectors (diagonalization of A)gridplot definitions (only need to use, not understand code)This modifies the command plot_plus_grid by Klaus Volpert from the gridlines worksheet:
http://www.math.villanova.edu/archives/maple/misc/gridline.mwsgrid_plot:=proc(a,b,c,d, m,n)
local i,j,v,h, p, ai, bi, ci,di,V,H;
#with(plots,display):
ai:=ceil(a): bi:=floor(b): ci:=ceil(c): di:=floor(d):
V:=[];
for i from ai to bi by m do
v[i]:= plot([i,t,t=c..d], thickness=0, color=black, linestyle=2):
V:=[op(V),v[i]];
od:
H:=[];
for j from ci to di by n do
h[j]:= plot([t,j,t=a..b], thickness=0, color=black, linestyle=2):
H:=[op(H),h[j]];
od:
plots[display]([op(V), op(H)]);
end;new_grid_plot:=proc(X,Y,a,b,c,d, m,n)
local i,j,v,h, p, ai, bi, ci,di,V,H;
#with(plots,display):
ai:=ceil(a): bi:=floor(b): ci:=ceil(c): di:=floor(d):
V:=[];
for i from ai to bi by m do
v[i]:= plot([i*X[1]+t*Y[1],i*X[2]+t*Y[2],t=c..d], thickness=0, color=blue, linestyle=1,thickness=1):
V:=[op(V),v[i]];
od:
H:=[];
for j from ci to di by n do
h[j]:= plot([t*X[1]+j*Y[1],t*X[2]+j*Y[2],t=a..b], thickness=0, color=blue, linestyle=1,thickness=1):
H:=[op(H),h[j]];
od:
plots[display]([op(V), op(H)]);
end;This helps visualize the coordinate system associated with a new basis of the plane:display(
grid_plot(-6.5,7.5, -2.5,8.5,1,1), # EDIT window
new_grid_plot([1,1],[-1,2], # EDIT new basis vectors
-3.5,4.5,-3.5,3.5,1,1),scaling=constrained); gridplots:=%:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The coefficient matrix: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 inverse matrix takes us from the old coordinates to the new coordinates.eigenvectors by handLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWFjdGlvbkdGJDYkLUkobWZlbmNlZEdGJDYoLUYjNigtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtRiM2KS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GYG8tSSNtbkdGJDYkUSMxMEYnRjkvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRicvJStleGVjdXRhYmxlR0Y9LyUpcmVhZG9ubHlHRjEvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0Y5LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0ZicC8lK2dyb3VwYWxpZ25HRmJwLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRmlwLUZobjYoLUZjbzYkRmlwRjlGYHBGY3BGZXBGZ3BGanBGYHBGY3BGZXAtRmVuNictRmhuNigtRmNvNiRRIjJGJ0Y5RmBwRmNwRmVwRmdwRmpwLUZobjYoLUYjNilGXG8tRmNvNiRRIzExRidGOUZmb0Zpb0ZbcEZdcEY5RmBwRmNwRmVwRmdwRmpwRmBwRmNwRmVwLyUmYWxpZ25HUSVheGlzRicvRmFwUSliYXNlbGluZUYnL0ZkcFEmcmlnaHRGJy9GZnBRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0YxLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGW3MvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGZnMvJSZmcmFtZUdGZnMvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Y9LyUtZXF1YWxjb2x1bW5zR0Y9LyUtZGlzcGxheXN0eWxlR0Y9LyUlc2lkZUdGZHIvJTBtaW5sYWJlbHNwYWNpbmdHRmNzRmZvRmlvRltwRl1wRjlGOS9JK21zZW1hbnRpY3NHRiRRJ01hdHJpeEYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmh0LyUrYWN0aW9udHlwZUdRLnJ0YWJsZWFkZHJlc3NGJy1GLDYjRmJwRmlvRjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEoQWxhbWJkYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRIkFGJ0YvRjItRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZWLUYsNiVRJyYjOTIzO0YnL0YwRj1GOS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORmpuLUYjNictRiw2I1EhRictSShtYWN0aW9uR0YkNiQtRiM2J0Zeby1GIzYnRl5vLUZibzYkLUkobWZlbmNlZEdGJDYoLUYjNidGXm8tSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtRiM2Ji1JI21uR0YkNiRRIjFGJ0Y5LyUrZXhlY3V0YWJsZUdGPS8lLHBsYWNlaG9sZGVyR0YxRjkvJSlyb3dhbGlnbkdGYG8vJSxjb2x1bW5hbGlnbkdGYG8vJStncm91cGFsaWduR0Zgby8lKHJvd3NwYW5HRl1xLyUrY29sdW1uc3BhbkdGXXEtRmZwNigtRiM2Ji1GW3E2JFEiMEYnRjlGXnFGYHFGOUZicUZkcUZmcUZocUZqcUZicUZkcUZmcS1GY3A2J0ZcckZlcEZicUZkcUZmcS8lJmFsaWduR1ElYXhpc0YnL0ZjcVEpYmFzZWxpbmVGJy9GZXFRJ2NlbnRlckYnL0ZncVEnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHRjEvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0Zicy8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0ZddC8lJmZyYW1lR0ZddC8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRj0vJS1lcXVhbGNvbHVtbnNHRj0vJS1kaXNwbGF5c3R5bGVHRj0vJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGanNGXm9GXnFGOUY5L0krbXNlbWFudGljc0dGJFEnTWF0cml4RicvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGYHUvJSthY3Rpb250eXBlR1EucnRhYmxlYWRkcmVzc0YnRl5vRl5xRjlGXm9GL0YyRml1Rl5vRl5xRjlGXm9GXnFGOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2KVEoU3R1ZGVudEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVib2xkR1EmZmFsc2VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStleGVjdXRhYmxlR0Y0LyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjFRIzotRidGL0YyRjhGOy9GPlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZWLUYsNilRLkxpbmVhckFsZ2VicmFGJ0YvRjJGNUY4RjtGPUZALUYsNilRLERldGVybWluYW50RidGL0YyRjVGOEY7Rj0tSShtZmVuY2VkR0YkNigtRiM2Ki1GQTYxUSJ+RidGL0YyRjhGO0ZERkZGSEZKRkxGTkZQRlJGVEZXLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRZG8+SShBbGFtYmRhRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHNiIiNXknXEVQdVN1WSU9RicvJSthY3Rpb250eXBlR1E7bWFwbGVzb2Z0LmNvbTpsYWJlbChMMzMwNylGJy8lJXZpZXdHUSZsYWJlbEYnRl5vRi9GMkY4RjtGREYvRjJGOEY7RkQtRkE2MVEiPUYnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSL0ZVUSwwLjI3Nzc3NzhlbUYnL0ZYRmJwLUkjbW5HRiQ2KFEiMEYnRi9GMkY4RjtGREYvRjJGOEY7RkQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KVEmc29sdmVGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNigtRiM2KS1JI21vR0YkNjFRIn5GJ0YvRjJGOEY7L0Y+USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmVuLUYsNilRIiVGJ0YvRjIvRjZGNEY4RjtGSUYvRjJGOEY7RklGL0YyRjhGO0ZJRi9GMkY4RjtGSQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Ki1GLDYlUScmIzkyMztGJ0YvRjItSSNtb0dGJDYtUSI9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlEtRj42LVEqJnVtaW51czA7RidGMkZBRkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRlgtSSNtbkdGJDYkUSI5RidGMi1GPjYtUSIsRidGMkZBL0ZEUSV0cnVlRidGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTUSwwLjMzMzMzMzNlbUYnLUYsNiVRKEFsYW1iZGFGJ0YvRjIvJStleGVjdXRhYmxlR0YxRjJGMi1GPjYtUSI7RidGMkZBRltvRkVGR0ZJRktGTUZdb0ZSLUY+Ni1RIn5GJ0YyRkFGQ0ZFRkdGSUZLRk1GXW8vRlNGXm8tRiw2JVE2UmVkdWNlZFJvd0VjaGVsb25Gb3JtRicvRjBGXG8vRjNRJ2l0YWxpY0YnLUY2NiQtRiM2JS1GLDYlUSIlRidGYHBGYXBGZG9GMkYyRmZvRmlvLUY2NiYtRiM2J0ZncC1GPjYtUSJ8Z3JGJ0YyRkFGQy9GRkZcb0ZHRklGS0ZNL0ZQUSwwLjExMTExMTFlbUYnL0ZTRmNxLUY2NiYtRiM2Jy1GZW42JFEiMEYnRjJGaG5GaXFGZG9GMkYyLyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0Zkb0YyRjJGXHJGX3JGZm9GaW8tRiw2JVEzQmFja3dhcmRTdWJzdGl0dXRlRidGYHBGYXBGY3BGZG9GMg==So LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY0RjQvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnRjQ= is an eigenvector basis for this eigenspace.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So 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 is an eigenvector basis for this eigenspace.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Now we evaluate the new components of the initial position.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So the new coordinates are LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiM0YnRjRGNEY0LyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0Y0. We check this linear combination of the new basis vector.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 general solution is a linear combination of these eigenvectors with coefficients which are exponentials whose rate coefficients are the eigenvalues. The coefficients are the new coordinates of the initial position.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The two characteristic times are 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. The bigger one determines the longer decay.The first coordinate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ decays to the one percent level in 4.6 characteristic timesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRJDQuNkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiRRIjlGJ0YyLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRC8lKWJldmVsbGVkR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRklGMg==Now we do the DEplot but since I have to provide the answer key as a PDF, I will use Maple to annotate the plot and draw the parallelogram. You only need to do the basic plot and print it out and use a pencil or pen to complete it.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Now for the direction field with the eigenvectors and new coordinate axes, and the parallelogram projection of the initial vector along those axes.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRkM2LVEifkYnRkBGRkZIRkpGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZnbkYrLUY2NiQtRiM2JS1GLDYlUShERXRvb2xzRidGL0YyRj1GQEZARkJGPUZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEoV2luZG93eEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZTLUkjbW5HRiQ2JFEiM0YnRjktRjY2LVEjLi5GJ0Y5RjtGPkZARkJGREZGRkhGUi9GTlEmMC4wZW1GJy1GVjYkUSI4RidGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLRmduRmZuLUYsNiVRKFdpbmRvd3lGJ0YvRjJGNUZPLUZWNiRRJDQuNUYnRjlGWS1GVjYkUSI1RidGOUZbby8lK2V4ZWN1dGFibGVHRj1GOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZobi1JI21pR0YkNiVRJWRlcXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlMtRiw2JVEjeDFGJ0YvRjItRjY2LVEiJ0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4xMTExMTExZW1GJ0ZULUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEidEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRk8tSSVtc3ViR0YkNiUtRiw2JVEiQUYnRi9GMi1GIzYnLUkjbW5HRiQ2JFEiMUYnRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZSL0ZOUSwwLjMzMzMzMzNlbUYnRlxwRl9vRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYuRlFGL0YyRjtGPkZARkJGREZGRkhGUkZURlVGZ24tRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZfcS1GZW82JUZnby1GIzYoRlxwRmBwLUZdcDYkUSIyRidGOUZPRl9vRjlGZnAtRiw2JVEjeDJGJ0YvRjJGZ25GYHBGaHFGWEZnbkZhby1GZW82JUZnby1GIzYnRmVxRmBwRlxwRl9vRjlGZnBGT0ZVRmduRmlwLUY2Ni5GXXFGL0YyRjtGPkZARkJGREZGRkhGXnFGYHEtRmVvNiVGZ28tRiM2J0ZlcUZgcEZlcUZfb0Y5RmZwRk9GaHFGZ24tRjY2LVEiO0YnRjlGO0ZjcEZARkJGREZGRkhGUkZNLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlMvJSZkZXB0aEdGXXMvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2JVElcGxvdEYnRi9GMi1GaG42JC1GIzY5LUZobjYmLUYjNitGTy1GLDYlUSJ4RidGL0YyRmBwLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZecUZgcUZlcUZPRmB0Rl9vRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZgcEZgdEZhby1GLDYlUShXaW5kb3d4RicvRjBGPUY5RmBwLUYsNiVRJmNvbG9yRidGL0YyRmFvLUYsNiVRJmdyZWVuRidGL0YyLUY2Ni5GYnBGL0YyRjtGY3BGQEZCRkRGRkZIRlJGZHAtRiw2JVEqdGhpY2tuZXNzRidGL0YyLUY2Ni5GY29GL0YyRjtGPkZARkJGREZGRkhGSkZNLUZdcDYlRmdxRi9GMkZmdS1GLDYlUSV2aWV3RidGL0YyRmFvLUYsNiVRKFdpbmRvd3lGJ0ZfdUY5RmBwLUYsNiVRJ2xhYmVsc0YnRi9GMkZbdi1GaG42Ji1GIzYoLUYsNiNRIUYnLUkjbXNHRiRGXXdGZnVGX3dGXHdGOUY5RmZ0Rml0Rl9vRjlGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUZoci1GaXI2JkZbc0Zec0Zgcy9GY3NRJWF1dG9GJ0Zlcy1GaG42JC1GIzYoLUZobjYmLUYjNistRiw2JVEoY29udmVydEYnRi9GMi1GaG42JC1GIzYoLUZdcDYkUSI0RidGOUZPLUYsNiVRI2IxRidGL0YyRmBwLUYsNiVRJWxpc3RGJ0YvRjJGOUY5RmBwRmB4LUZobjYkLUYjNixGZ3hGT0ZqeC1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRl5xRmBxRmVxRk8tRiw2JVEjYjJGJ0YvRjJGYHBGXXlGOUY5RmBwRmB4LUZobjYkLUYjNilGY3RGZXFGT0ZneUZgcEZdeUY5RjlGOUY5RmZ0Rml0RmBwRmB1RmFvLUYsNiVRJWdyYXlGJ0YvRjJGOUY5RmF3Rk9GaHJGaHItRiw2JVEnREVwbG90RidGL0YyLUZobjYkLUYjNj0tRmhuNiYtRiM2JUYrRl9vRjlGOUZmdEZpdEZgcC1GaG42Ji1GIzYpRlx3LUYjNidGVS1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGUkZURmduRl9vRjlGYHAtRiM2J0ZocUZiW2xGZ25GX29GOUZcd0Zfb0Y5RjlGZnRGaXRGYHBGXG9GYW8tRl1wNiRGaHBGOS1GNjYtUSMuLkYnRjlGO0Y+RkBGQkZERkZGSEZecUZURlxwRmBwRlVGYW9GT0ZcdUZgcEZocUZhb0ZidkZgcC1GaG42Ji1GIzYlLUZobjYmLUYjNi1GVS1GaG42JC1GIzYlRmdbbEZfb0Y5RjlGYW8tRl1wNiRRIjZGJ0Y5RmBwRmhxRmRcbEZhb0ZnW2xGX29GOUY5RmZ0Rml0Rl9vRjlGOUZmdEZpdEZgcEZPLUYsNiVRKGRpcmdyaWRGJ0YvRjJGYW8tRmhuNiYtRiM2Jy1GXXA2JFEjMjFGJ0Y5RmBwRmJdbEZfb0Y5RjlGZnRGaXRGX29GOUY5RmF3RmhyLUYsNiZRKGRpc3BsYXlGJ0YvRl9vRjItRmhuNiUtRiM2My1GLDYlUSQlJSVGJ0YvRjJGYHAtRiw2JVEjJSVGJ0YvRjJGYHAtRiw2JVEiJUYnRi9GMkZgcC1GLDYlUSNhMUYnRi9GMkZgcC1GLDYlUSNhMkYnRi9GMkZgcC1GLDYlUSNhM0YnRi9GMkZgcC1GLDYlUSNhNEYnRi9GMkZgcC1GLDYlUSNhNUYnRi9GMkZfb0Y5Rl9vRjlGYXctRiw2JUZnXWxGL0YyLUZobjYlLUYjNjpGXF5sRmBwRl9ebEZgcEZiXmxGYHBGZV5sRmBwRmhebEZgcEZbX2xGYHBGXl9sRmBwRmFfbEZgcEZfdkZhby1GaG42Ji1GIzYmRlx1RmBwRmJ2RjlGOUZmdEZpdEZgcC1GLDYlUSpncmlkbGluZXNGJ0YvRjJGYW8tRiw2JUYxRi9GMkY5Rl9vRjlGZXJGaHJGZHdGaHJGXHdGX29GOQ==JSFHThe arrows line up along the eigendirections as they should. Arrows point towards origin along those lines, indicating negative eigenvalues.e)
These are the actual solution curves versus time, needed for the final part.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=summary of 9 required plotsMaple 18 is misbehaving with the plot drawing tools for annotations. Will fix this later, maybe.1c,e. plots 1 and 3:
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pixels merge by this time,
amplitude \342\211\210 13.5 looks right
1d plot 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peak, maximum displacement at (1.095,0.257)1f,i. plots 3 and 4:
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 90 degrees out of phase (1/4 cycle),
response blue lagging behind (later in time),
characteristic of near resonanceLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEnJiM5Njk7RicvRjVRJmZhbHNlRicvRjhRJ25vcm1hbEYnRkRGREZERitGRA==/ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRRj5GPkY+
green is the natural frequency (3.04,3.04)
blue is the peak frequency (3.13,3.08)
2e. plot 6; 3d plot 7
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for viewing window
note initial conditions on vertical axis!yellow solution curve approaches origin quickly,
reaches the one percent level of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ at about time 0.55JSFH
3f. plots 8 and 9:
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 variables relax to 0
4.6 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global max shown forLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRi9GTUZQLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGLw==
pledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet stapled on top of your answer sheets as a cover page, with the first test page facing up:"During this examination, all work has been my own. I have read the long instructions on the class web page. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: