Problem $2.[30$ points$]$ Consider a mass$-$spring$-$damper system as we described in Lecture $17.$ The initial displacement of the mass is $r(0)=0\mathrm{.}5m$ and its initial velocity is $v(0)=1\mathrm{.}0\frac{m}{s}.$ A force of $1$ N is applied for the first $4$ seconds. The system has the following parameters:

$k=4$;$,\%$ spring coefficient$\frac{N}{m}$

$b=1$;$,\%$ damper coefficient $N.\frac{s}{m}$

$m=1$;$,\%$ mass $inkg$

Plot $r(t)$ vs$.t$ and $v(t)$ vs$.t$ on the same plot for a period of $30$ seconds with $5001$ samples.

Report your plot in the write$-$up$.$

Please submit your $.$m file as "yourLastName hw$12$ prob$3.$m$"$ with all the MATLAB commands you used.