The nonlinear second-order differential equation x 2kx c(x) 3 v2 x 0 arises in modeling
Chapter 11, Problem 22(choose chapter or problem)
The nonlinear second-order differential equation
\(x^{\prime \prime}-2 k x^{\prime}+c\left(x^{\prime}\right)^{3}+\omega^{2} x=0\)
arises in modeling the motion of an electrically driven tuning fork. See FIGURE 11.R.2, where k=c=0.1 and \(\omega=1\). Assume that this differential equation possesses a Type I invariant region that contains (0, 0). Show that there is at least one periodic solution.
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