Find your rhythm

Pendulum explorer

Change length and gravity to discover what controls a pendulum’s period.

Pendulum explorerTRY IT YOURSELF
L = 1 mθ = -10°
1.00 s
Period2.006 s
Frequency0.498 Hz
Angle now-10 °
Length1 m
Teal + amber · follow the changing valuesIdealized physics model

What if you changed…

Try a starting point

YOUR NEXT AHA

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

See the calculation

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

What this model assumes

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

Keep an eye on this

Large swings have a longer period than the small-angle approximation predicts.

Understand the physics ↗
A little question. A clearer picture.

Pendulum explorer: common 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.