The Simple Pendulum

For small oscillation angles, the period of a simple pendulum depends only on its length and the local gravitational acceleration - not its mass or amplitude: T = 2π√(L/g).

What affects the period?

Variable	Effect on period T
Length (L) doubled	T increases by √2 ≈ 1.414× (period gets ~41% longer)
Gravity (g) doubled (e.g., Jupiter)	T decreases by √2 (period gets ~41% shorter)
Mass doubled	No effect - mass cancels out in the formula
Small amplitude (angle <15°)	No significant effect - the small-angle approximation holds
Large amplitude (angle >30°)	Period increases slightly; exact solution requires an elliptic integral

Foucault pendulum and Earth's rotation

A Foucault pendulum swings freely while the Earth rotates beneath it, causing the plane of oscillation to appear to rotate over hours. At the North or South Pole it completes one full rotation per 24 hours. At latitude φ, the rotation rate is 360° × sin(φ) per day. This was the first direct visual demonstration of the Earth's rotation (Léon Foucault, Paris 1851).

Pendulums in timekeeping

The "seconds pendulum" has a period of exactly 2 seconds (one second per swing): its length at sea level is approximately 99.4 cm (nearly 1 meter). This is no coincidence - the meter was originally defined in the 1790s partly with the seconds pendulum in mind, though the final definition was set from a meridian measurement instead. Pendulum clocks dominated precision timekeeping from the 1650s (Huygens) until quartz oscillators replaced them in the 1930s–40s.