Motion of a Disk Hanging from a Spring on an Inclined Plane

A disk of variable radius and mass rolls down an inclined plane without slipping. The disk is attached at its center to a spring at the top of the plane. Initially, the disk is held so the spring is at its natural unstretched length. Once the system is released the disk is free to move under the influence of gravity.
Note that the motion of the disk does not change as the radius increases.


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Developed from the teaching materials of Thomas Peacock and David Gossard for Course 2.003 in the Department of Mechanical Engineering at MIT.
The equation of motion of the disk is .
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