Pendulum Simulator

The pendulum is the classic oscillator: gravity provides a restoring force that always pulls the bob back toward the bottom. For small swings, the motion is simple harmonic — and remarkably, the period depends only on the string length and gravity, not on the mass or (for small angles) the amplitude. That is why pendulums made such reliable clocks.

Controls

• String length: Length of the string from pivot to bob center, in meters.
• Bob mass: Mass of the swinging bob, in kilograms.
• Release angle: Starting displacement from vertical, in degrees.
• Play / pause: Start or pause the swing.
• Reset: Return the bob to the release position.

The physics

Assumptions

• Small swing angles (under ~15°) for the simple formula
• Massless, inextensible string
• Point-mass bob
• No air resistance or pivot friction

Guided activity

1. Fix the length at 1 m and measure the period by timing 10 swings.

2. Double the length. By what factor does the period change? Check the square-root law.

3. Change the mass while keeping length fixed. What happens to the period?

4. Pull the bob to a large angle (over 30°) and watch the period drift — when does the small-angle rule break?

Challenge questions

1. Why does the mass cancel out of the period formula? Trace it through the forces.

2. Design a pendulum with a 2-second period. What length do you need?

3. Explain why pendulum clocks run slow in summer — which quantity in the formula changes?