Problem $2$:

Consider the mechanical system shown in Fig. $2$ with a motor lifting a mass through a cable

and a pulley. Assume that the pulley is rigidly coupled to the motor shaft and the motor has

viscous friction with coefficient $B.$

${}_m$ is the applied motor torque, R is the pulley radius, M is the mass of the load, $J_m$ is the

motor inertia, and $J_p$ is the pulley inertia.

Write the equations of motion of the system.

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