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Please explain the working of a simple pendulum?
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.
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