For the given mechanical system

$($a$)[5$ pts$]$ Draw the free$-$body diagrams of interest

$($b$)[5$ pts$]$ Write the equations of motion

$($c$)[15$ pts$]$ Assuming the forcing function f$($t$)=5$u$($t$)($step$),$ find the closed$-$form$/$analytical solution for x$1($t$).$ Evaluate and plot the resulting function for the time interval t $=[0,10]$ seconds.

$($d$)[15$ pts$]$ Numerically solve the equations of motion found in part $($b$)$ for the same time interval as in part $($c$),$ plot and compare the results.