Consider t he system shown below. The masses are sitting on frictionless rollers.

$($a$)[6$ marks$]$ Find the equations of motion in the Laplace domain and express as a linear system in the form Ax $=$ b$.$

$($b$)[3$ marks$]$ Suppose that all masses are $1$ kg and all springs are linear with spring constants of $1$ N$/$m$.$ Find the transfer function X$3($s$)$F$($s$).$ Express the transfer function in standard form $($i$.$e$.,$ a fraction where numerator and denominator are polynomials in s$).$