Please use equivalent inertia and equivalent torque thank you. A rotor of a motor with viscous torsional damping $c_T$ and inertia $I_1$ is acted upon by a torque $T_1.$ The rotor is connected to a geartrain with gears of inertia $I_{G1}$ and $I_{G2}$ where the first gear turns $N$ times faster than the second gear $($i$.$e$.,$ the radius of gear $2$ is $N$ times bigger than the radius of gear $1).$ The second gear is connected to a drum of radius $R$ with inertia $I_2$ with an inextensible rope around it pulling on a mass $m.$ All shafts may be assumed to be rigid.

Find the equation of motion of the system in terms of the angle of the rotor, ${}_1.$