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 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.

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.

A pendulum comprising a light string of length L and small sphere, swings in the vertical plane . The string hits a peg located a distance of bellow the point of suspension (figure). If the pendulum is released from rest at the horizontal possition (theta = 90^(@)) and is to swing in a complete circule centered on the peg, the minimum value of d is

A heavy small sized sphere is suspended by a string of length l . The sphere rotates uniformly in a horizontal circle with the string making an angle theta with the vertical. Then the time period of this conical pendulum is-

The bob of a simple pendulum of length l is released from a point in the same horizontal line as the point of suspension and at a distance l from it Calculate the tension in the string at the lowest point of its swing (b) If the string of the pendulum is catched by a nail located verticaly below the point of suspensions and the bob just swings around a complete circle around the nail, find the distance of the nail from the point of suspension (c) If the string of the pendulum is made of rubber then show that it will be stretched by 3 mg//k on reaching the bob at the lowest point. Here k is the force constant of the string