Problem $3$:

Consider the mechanical system shown in Fig. $3$ with one mass $M_1$ sliding on an inclined

plane $($with angle $)$ and connected to a spring with a stiffness K $.$ The mass is lifting another

mass $M_2$ through a rigid cable and a pulley with radius $R$ and inertia $J_p.$ Assume that the

pulley and mass $M_1$ have negligible frictions.

Write the equations of motion of the system.

Combine the equations and find the equivalent differential equation as a function of $.$

Describe the motion of the system.

Fig. $3$