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Simple Pendulum

A pendulum is any system where a mass is allowed to swing freely around a pivot. A child swinging on a tyre swing, or your leg while walking are two examples. When a pendulum is moved from its equilibrium position, gravity provides the restoring force. A pendulum will display simple harmonic motion if the angle between its equilibrium position and its maximum displacement is small (less than 15 degrees). For a child on a tyre swing, the mass of the tyre plus child is much greater than the mass of the rope, so the mass of the rope can be ignored. This type of pendulum, where all of the mass is at some length, l, from the pivot is called a simple pendulum. The period of a simple pendulum undergoing simple harmonic motion is $$T = 2\pi \sqrt{\frac{l}{g}}$$ Notice that the period does not depend on the mass of the pendulum. So in the case of the tyre swing, its period would be the same whether the child was on the swing, or whether it was just the tyre swinging.

Investigate the following with the simulation

Show energy:
Frequency:
Damping:
Acceleration Perturbation (angle dependent)
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Initial Values
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