Chapter 4.6, Problem 24P

Suppose that the system of Problem 23 is modified to include a damping term and that the resulting initial value problem is

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

Plot a computer generated solution of the given problemfor several values of $\omega$ between $\frac{1}{2}$ and $2$, and estimate the amplitude, say $G_H\left(\omega \right)$, of the steady response in each case.

Using the data from part (a), plot the graph of $G_H\left(\omega \right)$ versus $\omega$. For what frequency $\omega$ is the amplitude greatest?

Compare the results (a) and (b) with the corresponding results for the linear spring.