Simple pendulum

An idealized oscillator consisting of a point mass suspended from a fixed pivot by a massless, inextensible string. Its motion is periodic for small angular displacements.

Pendulum equation: The differential equation describing a pendulum’s angular motion under gravity. It expresses how gravity and angular displacement determine the pendulum’s acceleration.
Angular displacement: The angle through which a body has rotated from a reference orientation. It specifies the bob’s position relative to the downward equilibrium direction.
Pendulum clock: A clock that uses a pendulum’s regular oscillations to regulate timekeeping. It applies the pendulum’s nearly stable period to divide time into intervals.
Physical pendulum: A rigid body that swings about a pivot under gravity, with its mass distributed across its shape. Unlike the simple pendulum, its rotational inertia depends on the body’s mass distribution.
Small-angle approximation: The approximation sin θ ≈ θ when θ is measured in radians and is small. It turns the pendulum’s nonlinear equation into the simple harmonic oscillator equation.
Angular frequency: The rate of change of phase in an oscillation, measured in radians per unit time. For small swings, it sets how quickly the pendulum cycles.
Gravimeter: An instrument that measures local gravitational acceleration or variations in gravity. A pendulum’s period can be used to estimate gravitational acceleration.
Compound pendulum: A rigid-body pendulum whose mass is distributed rather than concentrated at one point. It replaces the point-mass idealization with a body having finite rotational inertia.
Simple harmonic motion: Periodic motion in which restoring acceleration is proportional to displacement and points toward equilibrium. At small amplitudes, the simple pendulum is a physical example of this general motion.
Period: The time required for one complete cycle of a repeating motion. The simple pendulum’s period depends on its length and gravitational acceleration.

Linked from 8 pages