Consider a driven undamped spring/mass system described by the initial-value problem d +

Chapter 3, Problem 44

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Consider a driven undamped spring/mass system described by the initial-value problem d + w2 x = F0 sinn ')'t, x(O) = 0, x'(O) = 0. dt (a) For n = 2, discuss why there is a single frequency 1/27T at which the system is in pure resonance. (b) For n = 3, discuss why there are two frequencies ')'1/27T and 12 /27T at which the system is in pure resonance. (c) Suppose w = 1 and F0 = 1. Use a numerical solver to obtain the graph of the solution of the initial-value problem for n = 2 and')' = 'Yi in part (a). Obtain the graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to 'Y = 'Yi and')' = ')'2 in part (b).