Simple Pendulum: Harmonic Motion at Small Angles

A simple pendulum consists of a mass (called a bob) suspended from a fixed point by a string or rod, swinging back and forth under the influence of gravity. When displaced slightly from its resting position and released, it undergoes periodic motion.

For small angles (typically less than about 15°), the motion closely resembles simple harmonic motion (SHM) because the restoring force is approximately proportional to the displacement. This means:

  • The pendulum swings back and forth in a regular, repeating pattern
  • The period (time for one complete swing) depends only on the length of the pendulum and the acceleration due to gravity, not on the mass or amplitude (as long as the angle is small)

Why only small angles?
At larger angles, the motion becomes more complex because the restoring force is no longer linearly related to displacement, and the approximation of SHM breaks down.

Simple pendulums are classic tools in physics to study oscillations, energy conservation, and timekeeping.

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