Consider the model of an undamped nonlinear spring/mass
Chapter 5, Problem 8E(choose chapter or problem)
Consider the model of an undamped nonlinear spring/mass system given by \(x^{\prime \prime}+8 x-6 x^{3}+x^{5}=0\). Use a numerical solver to discuss the nature of the oscillations of the system corresponding to the initial conditions:
\(x(0)=1, x^{\prime}(0)=1 ; \quad x(0)=-2, x^{\prime}(0)=\frac{1}{2}\)
\(x(0)=\sqrt{2}, x^{\prime}(0)=1 ; \quad x(0)=2, x^{\prime}(0)=\frac{1}{2}\)
\(x(0)=2, x^{\prime}(0)=0 ; \quad x(0)=-\sqrt{2}, x^{\prime}(0)=-1\).
Text Transcription:
x^prime\prime+8x-6x^3+x^5=0
x(0)=1,x^prime(0)=1;x(0)=-2,x^prime(0)=frac12
x(0)=sqrt2,x^prime(0)=1;x(0)=2,x^prime(0)=frac12
x(0)=2,x^prime(0)=0;quadx(0)=-sqrt2,x^prime(0)=-1
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