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. Time after which the pendulum returns back to its initial position is

A simple pendulum of length l and mass m free to oscillate in vertical plane. A nail is located at a distance d=l-a vertically below the point of suspension of a simple pendulum. The pendulum bob is released from the position where the string makes an angle of 90^@ from vertical. Discuss the motion of the bob if (a) l=2a and (b) l=2.5a .

A simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle theta with the vertical, the angle theta which the acceleration vector of the bob makes with the string is given by–

A nail is located at a certain distance vertically below the point of suspension of a simple pendulum. The pendulum bob is released from a position where the string makes an angle of 60^(@) with the vertical. Calculate the distance of nail from the point of suspension such that the bob will just perform revolutions with the nail as centre. Assume the length of the pendulum to be one meter.