$4-3.$ Fig. $4$P$-3$ shows a simple model of a vehicle suspension system hitting a bump. If the mass of

the wheel and its mass moment of inertia are m and J$,$ respectively, then:

$($a$)$ Find the equation of the motion.

$($b$)$ Determine the transfer function of the system.

$($c$)$ Calculate its natural frequency.

$($d$)$ Use MATLAB to plot the step response of the system.