Pendula

Meet Pendula, a pendulum whose rhythm depends on her length, not on how heavy she is.

A simple pendulum is a small mass on a light string. When it swings, gravity pulls it back toward the lowest point. For small swings that restoring pull is nearly proportional to the displacement, so the motion is simple harmonic, with period T = 2π√(L/g). The mass cancels out, because a heavier bob feels more gravity but also needs more force to accelerate.

A 1 metre pendulum, with standard g = 9.80665 m/s², has a period of about 2.01 seconds. To double the period you need four times the length.

Galileo studied pendulums, and Christiaan Huygens built the first pendulum clock in 1656, which made clocks far more accurate. Because the period depends on g, pendulums were also used to measure small variations in gravity around Earth.

The formula is the small-angle approximation. At larger swings the period gets longer, by about 0.2 percent at 10° and more after that. Air drag and a heavy string also shift it.