Question

A uniform cylinder of mass M and radius R rolls without slipping down a slope of angle theeta to the horizontal. The cylinder is connected to a spring constant K while the other end of the spring is connected to a rigid support at P. The cylinder is released when the spring is unstrectched. The maximum displacement of cylinder is ?

Answer 1

The problem can be depicted as

such that the free body diagram for the cylinder can be shown as

Here, is the restoring force due to the spring. The potential energy of the cylinder at the initial point (highest point) on the slope is given by which will be balanced by the potential energy stored in the spring i.e. , where is the displacement of the spring from its rest position which is equal to the displacement of the cylinder. Hence, we can write