Pendel

Pendel is the German and Swedish term for a pendulum, a rigid body that is free to swing about a fixed pivot under the influence of gravity. In physics and engineering, a pendulum is a body attached to a pivot by a rod or string that allows rotational motion in a plane.

The simplest model is the simple pendulum: a point mass m at the end of a light, inextensible string of length L swinging in a vertical plane. For small swing angles, the period T is approximately T = 2π sqrt(L/g), where g is the local acceleration due to gravity. In this idealized case the period is largely independent of the mass and, to a first approximation, of the amplitude.

Variants include the physical pendulum, where the distributed mass affects the period and the moment of inertia I about the pivot, giving T ≈ 2π sqrt(I/(m g d)) with d the distance from the pivot to the center of mass. A torsion pendulum uses twisting rotation rather than linear swinging. Real pendulums experience damping and may be driven by external forces, as in clocks.

History and significance: pendulums have been studied since antiquity, with Galileo Galileo contributing to the understanding of isochronism. The pendulum clock, developed by Christiaan Huygens in the 17th century, relied on a swinging pendulum for timekeeping. Foucault’s pendulum demonstrated Earth’s rotation and remains a common physics demonstrator.

Applications span timekeeping, gravity measurement, seismology, and various precision instruments. The concept also informs the broader study of harmonic motion and oscillatory systems.