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 $R = 1 m$