A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance 3l//4 . The pendulum is released from rest. Throughout the motion the moving string makes small angle with vertical. Find the time after which the pendulum returns back to its initial position.

A pendulum has time period T for small oscillations. An obstacle P is

1.	A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance 3l//4 . The pendulum is released from rest. Throughout the motion the moving string makes small angle with vertical. Find the time after which the pendulum returns back to its initial position.
Answer» Solution :After P LENGTH of pendulum becomes `(1)/(4)` Now as `T prop SQRT(L)` , So after P time PERIOD will become `T^(1)= T//2`. Therefore, the DESIRED time will be : `t= (T)/(2)+ (T)/(2)= (T)/(2)+ (T)/(4)= (3T)/(4)`