Consider a driven undamped spring/mass system described by
Chapter 5, Problem 44E(choose chapter or problem)
Consider a driven undamped spring/mass system described by the initial-value problem
\(\frac{d^{2} x}{d t^{2}}+\omega^{2} x=F_{0} \sin ^{n} \gamma t, \quad x(0)=0, \quad x^{\prime}(0)=0\)
(a) For n = 2, discuss why there is a single frequency \(\gamma_{1} / 2 \pi\) at which the system is in pure resonance.
(b) For n 3, discuss why there are two frequencies \(\gamma_{1} / 2 \pi\) and \(\gamma_{2} / 2 \pi\) at which the system is in pure resonance.
(c) Suppose \(\omega=1\) and \(F_{0}=1\). Use a numerical solver to obtain the graph of the solution of the initial-value problem for n = 2 and \(\gamma=\gamma_{1}\) in part (a). Obtain the
graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to \(\gamma=\gamma_{1}\) and \(\gamma=\gamma_{2}\) in part (b).
Text Transcription:
fracd^2xdt^2+omega^2x=F_0\sin^ngammat,x(0)=0,x^prime(0)=0
gamma_1/2pi
gamma=gamma_1
omega=1
F_0=1
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