Consider the mechanical system shown in Fig. $1.$ Dr$.$ Wu is also interested in Let be

the displacement of the left member of the spring and the displacement of the mass.

Hence two new unknown variables are added to the system: $x_1(t)inR$ and $x_3$inR.

Figure $1$

$($a$)$ Sketch all $3$ free body diagrams.

$($b$)$ Derive $3$ the equations of motion $($EOM$)$ in time domain $.$