Pendules

Pendules is the French term for pendulums, which are devices consisting of a weight (the bob) suspended from a pivot so it can swing freely under gravity. In science and engineering, the simplest and most studied form is the simple pendulum, where a point mass is attached to a lightweight string or rod. The motion is governed by gravity and the geometry of the setup, and can be analyzed as a rotating system around the pivot.

The idealized equation of motion shows that for small angular displacements, the pendulum behaves like a simple harmonic oscillator with period T ≈ 2π√(L/g), where L is the length of the string and g is the local gravitational acceleration. Real pendulums experience damping and may be driven by external forces, leading to a decaying amplitude or a steady oscillation under forcing. The general equation is θ'' + (b/mL^2)θ' + (g/L)sinθ = 0, highlighting how angle, length, and friction influence behavior.

Beyond the simple pendulum, there are physical or compound pendulums, where the swinging body has extended mass. In a physical pendulum, the period is T = 2π√(I/(m g d)), with I the moment of inertia about the pivot and d the distance from the pivot to the center of mass. These forms explain a wide range of real-world devices and experiments.

Applications include timekeeping in pendulum clocks, seismology and gravity studies, and demonstrations of Earth’s rotation, notably the Foucault pendulum. Historically, pendulums contributed to ideas about isochronism and gravity, with notable early work by Galileo and Christiaan Huygens. The term pendules is the French plural for pendulum.