Two masses m $1$ and m $2$ are connected by a spring with spring constant $k,$ as shown in

the figure. Assuming no friction, derive a state$-$space representation of the system,

which is at rest for The displacements y $1$ and y $2$ are the outputs of the system and

are measured from their rest positions relative to the ground.

Assuming that $m1=40kg,m2=100kg,k=40\frac{N}{m},$ and f is a step force input of

magnitude of $10$ N $,$ obtain the response curves y $1(t)$ versus $t$ and $y2(t)$ versus $t$ with

MATLAB. Assume that we are interested in the period $0t20.$