In the figure, the car window opening system is driven by a pulley system. The rollers are fixed and the glass is moved up and down

with plastic holders by means of belts.

With the pulley rotation angle $$ the rope speed in the system will be expressed as $r^{**}.$ Pulley diameters $r$ can be taken as half

diameter. In this system, glass weight and pulley masses will be considered. Friction will be neglected. All required system properties

including mass moments of inertia and cycle ratios of the worm gear and spur gear pair will be determined parametrically by you

$($cycle ratios: $i_1,i_2,$ input angle $$ for example$).$

Write the reduced moment of mass inertia of the Dc motor shaft $(O_1)$ considering the elements that will affect the system kinetically

and kinematically. Obtain the differential equation governing the motion.