Tuesday, December 29, 2015

Speed of Simple Pendulum after Angular Displacement

Simple pendulum is a system which has point sized heavy mass suspended from a rigid support with a in extensible and mass less string. If it is slightly disturbed from mean position, it starts oscillating and executes simple harmonic motion. By default the pendulum is in a equilibrium position. This is treated as equilibrium position and is called reference position.

At the reference point, potential energy is treated as zero. If we displace the bob by applying a horizontal force, it deviates from mean position and goes to a particular position.

As the bob is displaced from mean position, it acquires a certain height from mean position. It has gone to that position as we have given some velocity at the mean position. We can understand that the body acquires some velocity as it has moved away from mean position. Here we are actually measuring kinetic energy by converting the potential energy and using law of conservation of energy.

Let us consider the bob of mass m is suspended with the string of length l and it is freely suspended. Let we have given some velocity u at the horizontal position by applying the force. As the body moves away from mean position, its velocity decreases.

The final velocity acquired by the body also will be in terms of angular displacement.

A detailed video is made here presented below.

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