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harsh mehta Grade: 12

Please explain the working of a simple pendulum?

8 years ago

Answers : (1)

Gaurav Sharma
19 Points

A Simple Pendulum



A simple pendulum is a pendulum with all the mass the same distance from the support point, like a ball on the end of a string. Gravity provides the restoring force (a component of the weight of the pendulum).


Summing torques, the restoring torque being the only one, gives:


For small angular displacements :


So, the torque equation becomes:


Whenever the acceleration is proportional to, and in the opposite direction as, the displacement, the motion is simple harmonic.

For a simple pendulum, with all the mass the same distance from the suspension point, the moment of inertia is:


The equation relating the angular acceleration to the angular displacement for a simple pendulum thus becomes:


This gives the angular frequency of the simple harmonic motion of the simple pendulum, because:


Note that the frequency is independent of the mass of the pendulum.

8 years ago
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