MAT2705-04/05 22S Quiz 9 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).1. 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 .a) Solve this IVP step by step.b) Express this solution in the form LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJBRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEidEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5Gam4tRiw2JVEkc2luRicvRjBGPUY5LUZTNiQtRiM2Jy1JJW1zdWJHRiQ2Ji1GLDYlUScmIzk2OTtGJ0Zfb0Y5LUYjNiUtRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmBwRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRidGZm5GV0ZaRjlGOUZaRjk= using the trig identity 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., where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA= is the envelope function for the faster oscillation in this beating problem, with envelope period LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW9HRiQ2L1EqJnVtaW51czA7RicvJSVib2xkR0Y0L0Y2USVib2xkRicvJStmb250d2VpZ2h0R0ZBLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy8lK2V4ZWN1dGFibGVHRkYvRjZRJ25vcm1hbEYn.c) Use Maple to plot the solution with the pair of envelope curves for 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 showing 2 beats and scan to include in your submitted quiz.
2. 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 , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIwRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQS1JI21vR0YkNi5RIj1GJ0YyRkEvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXRj1GMkZB, y '(0) = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JVEiMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRi9GMg== [Maple notation].
a) State Maple's solution of the initial value problem.b) Identify the values of the damping constant and characteristic time 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 , the natural frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Ji1JI21uR0YkNiVRIjBGJ0Y1RjcvRjNRJXRydWVGJ0Y1L0Y4USdpdGFsaWNGJy8lL3N1YnNjcmlwdHNoaWZ0R0Y/LUYvNiNRIUYnRjVGNw== , and the quality factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUklbXJvd0dGJDYlLUkjbW5HRiQ2JVEiMEYnRjJGNEYyRjQvJS9zdWJzY3JpcHRzaGlmdEdGPQ==LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEmJnRhdTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0YxLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JJW1yb3dHRiQ2JS1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0LyUvc3Vic2NyaXB0c2hpZnRHRj0=, exactly and numerically.
c) Find the general solution by hand, showing all steps (including the matrix solution steps).d) Find the solution satisfying the initial conditions, showing all steps.e) Express the steady state solution in phase-shifted cosine form. [Make sure you use a diagram to justify your values.] f) Now find the amplitude LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJyYjOTY5O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRj5GP0Y/RkFGPw== of the response function for the driving function 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 plot for \317\211=0..W where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiV0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y5USdub3JtYWxGJw== is the nearest integer to 5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiQtSSNtbkdGJDYlUSIwRidGNUY3RjcvJS9zdWJzY3JpcHRzaGlmdEdGPy1JI21vR0YkNi1RIi5GJ0Y3LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVkY1Rjc=g) Use calculus to find the exact frequency and amplitude of the resonance peak, and 3 decimal place decimal values.JSFHsolution1.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2.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv