$1.$ Derive the differential equation that describe the system output$-$input

signal relationship in time domain.

$2.$ From the answer of $1,$ derive the transfer function that describe the

relationship between displacement $($output$)$ to the net force $($applied force

F minus disturbance force FW$)$ in frequency$/$ s$-$domain.

$3.$ Assume the input F$=1000$ N u$($t$),$ M$=2\mathrm{.}5$ kg$,$ B$=1100$ N$/$ms$-1$ and spring

constant K$=1\mathrm{.}1$x$107$ N$/$m$,$ determine the displacement signal y$($t$)$

$4.$ Write m$-$file program to get the system response when a Unit step input

signal F$($t$)=1000$N u$($t$)$ is applied on the input. Change the damping

friction constant to a value so that the output will change to critical

damped, over$-$damped and critical stable.