Chapter 4.6, Problem 23P

A spring-mass system with a hardening spring (Section 4.1) is acted on by a periodic external force. In the absence of damping, suppose that the displacement of the mass satisfies the initial value problem

$y\text{'}\text{'}+y+0.2y^3=\cos \omega t,y\left(0\right)=0,y\text{'}\left(0\right)=0$.

Let $\omega =1$ and plot a computer generated solution of the given problem. Does the system exhibit a beat?

Plot the solution for several values of $\omega$ between $\frac{1}{2}$ and $2$. Describe how the solution changes as $\omega$ increases.