For the belt$-$driven system shown, $J_M$

and $J_L$ are motor and load inertias,

respectively, including pulley inertias.

$R_M$ and $R_L$ are the pulley radii and $B_M$

and $B_L$ are the viscous damping

coefficients for the motor and load,

respectively. Treat the belt as rigid,

i$.$e$.,$ neglect any belt compliance. Derive the equation of motion for the system first in terms

of ${}_M$ and then in terms of ${}_L.$ Show the equivalence of this system to the system in problem

#$2$ by comparing the equations of motion and transfer functions.