Chapter 17.3, Problem 11E

To determine

To show: If ${\omega }_0\ne \omega$, but $\frac{\omega }{{\omega }_0}$ is a rational number, then the motion described by $x\left(t\right)=c_1\cos \omega t+c_2\sin \omega t+\frac{F_0}{m\left({\omega }^2-{\omega }_0^2\right)}\cos {\omega }_{0}t$ is periodic.