A spring$-$mass$-$damper system is determined by m$=80$kg$,$k$=20$k$($N$)/($m$),$c$=250$

N$.($s$)/($m$),$ the system is subjected to the force F$($t$)=50$cos$(2$t$)$ in Newton.

The initial conditions x$\_(0)=0$m and v$\_(0)=0\mathrm{.}1($m$)/($s$)$ and the time x$1,$x$2,$v$10.$

a$.$ Using ode$45,$ find the solutions of the system

b$.$ Plot the displacement x$1$ and the velocity v$1$ on the same graph. Add a

legend.

c$.$ Plot the displacement x$1$ and the velocity v$1$ on the same graph if the initial

conditions are zeros. Add a legend.

d$.$ Open a new figure; plot, the displacement x$2$ if the system is free.

e$.$ Open a new figure; plot, on the same graph, the velocity v$1$ of the initial

system and the velocity v$2$ when the system is free.

f$.$ Open a new figure; using subplot, Plot the responses $($ x$1,$x$2,$v$1,$ and v$2).$

Give each curve a different color and put all the details on the graph $($x$-$axis,

y $-$axis, title, and legend$).$