Chapter 8.7, Problem 28E

To determine

To find: The displacement of the object of mass $m$ attached to a spring with spring constant $k$, if damping is $c\frac{dx}{dt}$, there is an external force $f\left(t\right)$ initial condition is $x\left(0\right)=0$, $x^{\prime }\left(0\right)=0$ and $m=1$, $k=13$, $c=4$, $f\left(t\right)=e^{-2t}$.