Chapter 5.8, Problem 1E

A software package that supports the construction of Poincaré maps is required for the problems in this section.

Compute and graph the points of the Poincaré map with $t=2\pi n$, $n=0,1,\mathrm{....},20$ for equation $\left(1\right)$, taking $A=F=1$, $\varphi =0$, and $\omega =3/2$. Repeat, taking $\omega =3/5$. Do you think the equation has a $2\pi$-periodic solution for either choice of $\omega$? A subharmonic solution?

$x^{″}\left(t\right)+{\omega }^{2}x\left(t\right)=F\cos t$, $\left(1\right)$