Oscillations 1

Classical Mechanics Level 5

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 \(R = 1 m\)

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