The model mx kx k1x3 F0 cos vt of an undamped periodically driven spring/mass system is
Chapter 3, Problem 11(choose chapter or problem)
The model \(m x^{\prime \prime}+k x+k_{1} x^{3}=F_{0} \cos \omega t\) of an undamped periodically driven spring/mass system is called Duffing's differential equation. Consider the initial-value problem \(x^{\prime \prime}+x+k_{1} x^{3}=5 \cos t\), x(0)=1, \(x^{\prime}(0)=0\). Use a numerical solver to investigate the behavior of the system for values of \(k_{1}>0\) ranging from \(k_{1}=0.01\) to \(k_{1}=100\). State your conclusions.
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