A pendulum has a period `T` for small oscillations. 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.

Explanation

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))`