Chapter 17.3, Problem 10E

To determine

To show: If external force $F\left(t\right)=F_0\cos \omega t$ is applied, then the motion of the mass is given by $x\left(t\right)=c_1\cos \omega t+c_2\sin \omega t+\frac{F_0}{2m\omega }t\sin \omega t$.