A spring$-$mass$-$damper system is determined by $m=100kg,k=10k\frac{N}{m},c=4000N.\frac{s}{m},$ the system is subjected to a force $E(t)$ in Newton. We will study the two following cases:

Part a$.$ F$1(t)=10cos(5t)$

Part b$.F2(t)=10$

The initial conditions $x_0=0m$ and $v_0=0\frac{m}{s}$ and the time $12v2x1,x2,v1xy0.$

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

$b.$ Plot the displacement $1$ and the velocity $v1on$ the same graph for part $a.$ Add a legend.

$c.$ Open a new figure; plot the displacements $2$ and $v2on$ the same graph for part $b.$ Add a legend.

$d.$ Open a new figure; plot, $on$ the same graph, the velocity $v1of$ the initial system and the velocity $v2.$ Write a legend.

$e.$ Open a new figure; using subplot, Plot the responses $(x1,x2,v1,$ and $v2).$

Give each curve a different color and put all the details $on$ the graph $(x-$axis, $y-$axis, title, and legend$).$