Question

A pendulum has a period `T` for small osillations. An obstacle is placed directly beneath the pivot, so that only the lowest one - quarter of the string can follow the pendulum bob when it swings to the left of its resting position. The pendulum is released from rest at a certain point. How long will it take to return to that point again ? In answering this question, you may assume that the angle between the moving string and the vertical stays small throughout the motion.

Answer 1

When the bob is located to the right of point O, the obstacle acts as the pivot. The effective length of the pendulum is `I//4` and when it is to to the left of obstacle the effective length is l
`implies t = (1)/(2) (2 pi sqrt((l)/(4k)) + 2 pi sqrt((l)/(g)))`
`implies t = (3T)/(4)`
where `T = 2 pi sqrt((l)/(g))`