QUESTION $4($SUPP EXAM$-$SEM$2-2019)$

A mechanical system is shown in Figure $5,$ where the input is the mechanical for $f(t)$ applied to the mass $M_1$ and the outputs are the displacement $x_1(t)$ of mass and displacement $x_2(t)$ of mass $M_2.$

Figure $5$: Mechanical system

$4\mathrm{.}1$ How many equations of motion does this mechanical system have? Justify answer.

$4\mathrm{.}2$Draw the free$-$body diagrams of this mechanical system $($all forces must be sho

$4\mathrm{.}3$Write the dynamic equations of this mechanical system in s$-$domain.

Find the transfer function $G(s)=\frac{x_2(s)}{F(s)}$