Now solved: Resonance and Beats. In Section 3.8 we observed that an undamped harmonic

Chapter 6, Problem 19

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Resonance and Beats. In Section 3.8 we observed that an undamped harmonic oscillator (such as a springmass system) with a sinusoidal forcing term experiences resonance if the frequency of the forcing term is the same as the natural frequency. If the forcing frequency is slightly different from the natural frequency, then the system exhibits a beat. In 19 through 23 we explore the effect of some nonsinusoidal periodic forcing functions.Consider the initial value problemy + y = f(t), y(0) = 0, y(0) = 0,wheref(t) = u0(t) + 2nk=1(1)kuk (t).(a) Draw the graph of f(t) on an interval such as 0 t 6.(b) Find the solution of the initial value problem.(c) Let n = 15 and plot the graph of the solution for 0 t 60. Describe the solutionand explain why it behaves as it does.(d) Investigate how the solution changes as n increases. What happens as n ?

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