A weight suspended from a pivot that swings back and forth under gravity.A pendulum is a weight suspended from a pivot so it can swing freely. When displaced from its equilibrium position, gravity provides a restoring force that causes it to oscillate back and forth. The period of a simple pendulum — the time for one complete swing — depends only on its length and the local gravitational acceleration, not on the mass of the bob or the amplitude (for small swings). This remarkable property makes pendulums precise timekeepers and sensitive instruments for measuring gravity.
Galileo Galilei observed the isochronism of pendulums around 1602, and Christiaan Huygens built the first pendulum clock in 1656. The theory was refined by Newton and later by mathematicians like Euler and Lagrange.
The pendulum's motion is governed by the balance between gravitational force (pulling the bob downward) and the tension in the string or rod (constraining it to move along an arc). For small angles, the motion is approximately simple harmonic: the restoring force is proportional to the displacement, leading to sinusoidal oscillations. The period is T = 2π√(L/g), where L is the length and g is gravitational acceleration. For larger amplitudes, the period increases slightly, a correction that can be calculated with elliptic integrals.
Pendulums are used in clocks, seismometers, and gravimeters; Foucault's pendulum demonstrates Earth's rotation. In modern physics, torsion pendulums measure weak gravitational forces and test the equivalence principle.
A pendulum's period is independent of the mass of the bob, which is why a heavier pendulum swings at the same rate as a lighter one of the same length.
