MAT2705-02/06 09F Quiz 8 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 arrows and equal signs 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).
1. 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
a) Use the method of undetermined coefficients to find the steady state sinusoidal solution (the particular solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRInBGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPQ== ) of this driven harmonic oscillator DE.
b) Evaluate the amplitude and phase shift of this steady state solution.c) Now consider a general positive frequency 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 . Find the steady state solution again.d) Evaluate the amplitude LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTY5O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj9GPw== of this sinusoidal function. Show that it simplifies to the formula 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.e) Use calculus to show that the peak amplitude occurs at the value LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYvNiNRIUYnRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1 \342\211\210 2.828. Evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+Rj5GPg==, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiM0YnL0YzUSdub3JtYWxGJ0Y+Rj5GPg== numerically.
f) Optional.
Use technology to plot LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRKCZvbWVnYTtGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRidGP0Y/Rj8= for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyLUY2Ni1RIy4uRidGMkY5RjtGPUY/RkFGQ0ZFL0ZIUSwwLjIyMjIyMjJlbUYnL0ZLUSYwLjBlbUYnLUZNNiRRIzIwRidGMkYy. Sketch what you see, labeling the axes, tickmarks and the vertical intercept and the points on the graph for which LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRJjIuODI4RidGMi1GNjYtUSIsRidGMkY5L0Y8USV0cnVlRidGPUY/RkFGQ0ZFL0ZIUSYwLjBlbUYnL0ZLUSwwLjMzMzMzMzNlbUYnLUZNNiRRIjNGJ0YyRjI=. solution1.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a)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About a fifth of a cycle to the right, so the first peak is behind in time compared to the standard cosine.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c)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using the matrix inverse to solve the linear system A C = b: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The tangent of the phase shift is given by this ratio which is zero at zero frequency. This was not requested,.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d)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e) the peak occurs at: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 that much (about 10 percent) below the natural frequency 3.16: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This is weakly damped.f) We go the extra mile by plotting the values at the peak and at \317\211=3 to show how close the corresponding points on the graph are.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=TTdSMApJNlJUQUJMRV9TQVZFLzE1MDg5MTQyNFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyUiIyIjLCYiIzUiIiIqJCUmb21lZ2FHIiIjISIiLCRGKyEiIywkRitGLEYnNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MjE3MDg3MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyIiIiIiITYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyMDEwOFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIyUiIyIjLCQqJiwmISM1IiIiKiQlJm9tZWdhRyIiI0YrRissKCIkKyJGK0YsISM7KiRGLSIiJUYrISIiRjQsJComRi1GK0YvRjRGLiwkRjYhIiNGJzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MjIyMDg4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIyUjQzNHJSNDNEc2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MjIzNzQ0MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiMiIywkKiYsJiEjNSIiIiokJSZvbWVnYUciIiNGK0YrLCgiJCsiRitGLCEjOyokRi0iIiVGKyEiIkY0LCQqJkYtRitGL0Y0Ri42Ig==