Simple Pendulum Calculator

The Physics of Timekeeping

Before atomic clocks and quartz watches, the entire world relied on a swinging weight on a string to tell time. This is the Simple Pendulum.

A "simple" pendulum is an idealized model in physics. It assumes a massless string, a frictionless pivot, and a bob (weight) that acts as a point mass.

The most amazing property of a pendulum is Isochronism: The time it takes to swing back and forth (the Period) is constant, regardless of how wide the swing is (for small angles).

The Formula ($T$)

The period depends on only two things: Length and Gravity.

• T (Period): Time for one full cycle (Left -> Right -> Left).
• L (Length): Length of the string in meters.
• g (Gravity): Acceleration due to gravity ($9.81 m/s^2$ on Earth).

The Galileo Story: Does Mass Matter?

In 1583, a young Galileo Galilei was sitting in the Cathedral of Pisa. He watched a chandelier swinging in the breeze. Using his own pulse to time it, he realized that the chandelier took the same amount of time to swing, whether it was swinging in a wide arc or a small arc.

He also realized something counter-intuitive: The weight of the chandelier didn't matter.

Length vs. Speed

Since gravity ($g$) is constant on Earth, the only way to change the speed of a pendulum clock is to change the Length ($L$).

• To slow it down: Make the string longer. (T increases).
• To speed it up: Make the string shorter. (T decreases).

To double the period (make it take twice as long), you must make the string 4 times longer, because the length is inside a square root ($\sqrt{L}$).

Gravity Matters: Clocks on the Moon

If you took a grandfather clock to the Moon, it would run very slowly.