Example $3\mathrm{.}1$ Plotting Free and Forced Vibrations

For the $1-$DOF system:

Figure $3\mathrm{.}3$: $1-$DOF spring$-$mass system subjected to an external force $F(t).$ with $k=10\frac{N}{m},m=2\mathrm{.}5kg,=4ra\frac{d}{sec,F_0}=0\mathrm{.}1N,x_0=1mm,$ and $v_0=0m\frac{m}{s}$ plot the temporal responses of the system considering the free$-$vibration case and the excited case. Plot these on a single plot to compare the responses.