Problem $3$: $[15$ pts$]$ Damped Harmonic Motion $(2\mathrm{.}2)$

Plot the response of the spring$-$mass$-$damper system with harmonic excitation described by

$$x$($t$)+2$n $$x$($t$)+$ w$2$

nx$($t$)=$ f$0$ cos t

with m $=1$ kg$,$ $=0\mathrm{.}1,$ n $=2$ rad$/$s$,$ f$0=3$ N$/$kg$,$ and $=10$ rad$/$s with initial conditions

x$0=1$ m$,$ v$0=1$ m$/$s for $30$ seconds