In the adjacent figure, a spring mass system $($ often called mechanical system independent of gravitational force$)$ is displayed.

$($a$)$ i$)$ Model the governing differential equation for the system $($using Newton's Law of motion$)$

ii$)$ Assume $m=1kg,k=1$ and $b=3$ then apply Laplace Transform to model the transfer function :$.$e; Y$($s$)/$U$($s$.$ Also, iii$)$ Solve for the transient performance specification i$.$e; i$)$ maximum overshoot, ii$)$ peak time, $($iii$)$ settling time and iv$)$ rise time.