Consider the initial value problemy+ y = h(t), y(0) = 0,

Chapter 6, Problem 23

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Consider the initial value problemy+ y = h(t), y(0) = 0, y(0) = 0,wheref(t) = u0(t) + 2nk=1(1)ku11k/4(t).Observe that this problem is identical to except that the frequency of theforcing term has been increased somewhat.(a) Find the solution of this initial value problem.(b) Let n 33 and plot the solution for 0 t 90 or longer. Your plot should show aclearly recognizable beat.(c) From the graph in part (b), estimate the slow period and the fast period for thisoscillator.(d) For a sinusoidally forced oscillator, it was shown in Section 3.8 that the slow frequencyis given by | 0|/2, where 0 is the natural frequency of the system and isthe forcing frequency. Similarly, the fast frequency is ( + 0)/2. Use these expressionsto calculate the fast period and the slow period for the oscillator in this problem. Howwell do the results compare with your estimates from part (c)?