Consider the initial value problem y__ + y = h(t), y(0) = 0, y_(0) = 0, where h(t) =

Chapter 6, Problem 17

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Consider the initial value problem y__ + y = h(t), y(0) = 0, y_(0) = 0, where h(t) = u0(t) + 2 n _ k=1 (1)ku11k/4(t). Observe that this problem is identical to 15, except that the frequency of the forcing term has been increased somewhat. a. Find the solution of this initial value problem. G b. Let n 33 and plot the solution for 0 t 90 or longer. Your plot should show a clearly recognizable beat. N c. From the graph in part b, estimate the slow period and the fast period for this oscillator. d. For a sinusoidally forced oscillator, it was shown in Section 3.8 that the slow frequency is given by 1 2 | 0|, where 0 is the natural frequency of the system and is the forcing frequency. Similarly, the fast frequency is 1 2 ( + 0). Use these expressions to calculate the fast period and the slow period for the oscillator in this problem. How well do