Pendulos

Pendulos, or pendulums, are devices in which a body suspended from a pivot swings under gravity, producing periodic motion. The simplest model is the simple pendulum, consisting of a point mass on a weightless, inextensible string of length L. Real pendulums include extended bodies (physical pendulums) where the distribution of mass affects the period. For small oscillations, the period is approximately T = 2π sqrt(L/g), with g the local gravitational acceleration. The motion is described by a nonlinear differential equation, and larger amplitudes cause deviations from the small-angle result. Damping and external driving yield a range of behaviors from steady oscillations to resonance or, in some cases, chaotic motion.

Historically, pendulums have played a central role in timekeeping and physics. Galileo noted that oscillation periods are nearly independent of amplitude, and Christiaan Huygens developed the first accurate pendulum clocks in the 17th century. The Foucault pendulum, demonstrated in 1851, provides a simple demonstration of Earth’s rotation.

Variants include torsional pendulums, compound (physical) pendulums, and driven or damped pendulums. Applications span time standards in clocks, gravity measurements with the seconds pendulum, seismology and geophysics, and educational demonstrations of harmonic motion and nonlinear dynamics. The term pendulum also appears in historical units and experiments; for example, the seconds pendulum, with a period of about two seconds, influenced clockmaking and gravitational studies.