The model of an undamped periodically driven spring/mass
Chapter 5, Problem 11E(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.
Text Transcription:
m x^prime\prime+k x+k_1x^3=F_0cosomegat
x^prime\prime+x+k_1x^3=5cost,x(0)=1,x^prime(0)=0
k_1>0
k_1=0.01
k_1=100
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