Oscillations 1

Consider a uniform ring of mass $$M$$ situated in the vertical plane. Another point mass $$M$$ is fixed to the ring at a point vertically below its centre. Consider the vertical diameter of the ring passing through the point mass. If the ring is pivoted at a point on the diameter let the time period of small oscillation be $$t$$. Find the distance (in meters) of this pivot from the centre of ring so that $$t$$ is minimum.

Details and Assumptions:

• Assume that the pivot is connected to the ring by light rods.
• Radius of ring $$R = 1 m$$
×