QUESTION $5($MAIN EXAM$-$SEM$2-2019)$

A mechanical system is given in Figure $7,$ where the input is the mechanical force $f(t)$ applied to the mass $M_2$ and the outputs are the displacement $x_1(s)$ of mass $M_1$ and displacement $x_2(s)$ of mass $M_2.$

Figure $7$: Mechanical system

$5\mathrm{.}1$ How many degrees of freedom does this mechanical system have? Justify your answer.

$5\mathrm{.}2$ Draw the free$-$body diagrams of this mechanical system $($all forces must be shown$).$

$5\mathrm{.}3$Write the dynamic equations of this mechanical system in s$-$domain.

Find the transfer function $G(s)=\frac{x_1(s)}{F(s)}$