Problem $4$

Consider the mass$-$spring$-$damper system at rest in Figure. The displacements $x_1$ and $x_2$ are

measured from their respective equilibrium positions.

$($a$)$ The input force $u(t)$ is applied to the system, and the displacement $x_l(t)$ is the output, obtaining

the transfer function $G(s)=\frac{x_1(s)}{U(s)}$ of the system.

$($b$)$ Suppose $m=2kg,k_1=k_2=1\frac{N}{m},c=1N\frac{s}{m}.$ Use MALAB to plot the step input $u(t)$ response

of the $x_l(t).$ Hint: Suggested functions are tf$()$ and step$($