The Physics of a Simple Pendulum

A simple pendulum is a mass on the end of a massless, rigid, frictionless string swinging under gravity. For small displacements the restoring force is proportional to the displacement itself, which produces perfect harmonic motion with a period that is independent of the mass and amplitude.

The Period Formula

T = 2π√(L/g) — the period depends on the square root of the length divided by gravity. Doubling the length multiplies the period by √2 ≈ 1.41; cutting gravity to a quarter doubles the period. This square-root behavior is what the chart visualizes.

From Swings to Clocks

Because the period is nearly constant regardless of how wide the pendulum swings, it became the world's first reliable timekeeper. A seconds pendulum — one that ticks exactly once per second — needs a length of about 0.994 m on Earth, a fact embedded in the design of every pendulum clock since Huygens built the first in 1656.