Find your rhythm

Pendulum explorer, explained.

For small angles, the restoring force gives approximately simple harmonic motion. The period grows with the square root of length and decreases with the square root of gravity. Bob mass cancels from the equation.

The relationship to remember

T = 2π√(L/g)

A worked example

At L = 1 m and g = 9.81 m/s², the period is about 2.01 s. Increasing length to 4 m doubles the period.

Inside the default experiment

T = 2π√(L/g) = 2π√(1/9.81) = 2.01 s.
Frequency = 1/T = 0.498 Hz.
Small-angle motion: θ(t) = 10 cos(2πt/T) degrees.

When this model applies

Small-angle approximation, massless rod/string, point bob, no damping. Angles are limited to 15°.

Make a prediction. Then test it.

Make the pendulum twice as slow. How much longer must it be?

Try the interactive experiment ↗

A little question. A clearer picture.

Frequently asked questions

Wondering about the why? Start here.

Does a heavier bob swing faster?

Not in this ideal pendulum model: mass cancels out. Length and gravity set the small-angle period.

Why does amplitude barely change the period?

The formula assumes small angles. The animation follows that approximation; for large angles, amplitude does affect period.