Pendulum Simulator
How to use the pendulum simulator
- Set the length, starting angle and gravity. The bob swings as soon as you change anything.
- Compare the measured period with the small-angle formula, then raise the starting angle past 60° to see them drift apart.
- Add damping to watch the swing die away, and read how much energy is left.
Frequently asked questions
What is the formula for the period of a pendulum?
For small swings, T = 2π√(L ÷ g): the period depends only on the length and gravity, not on the mass or the amplitude. A 1 m pendulum on Earth takes 2.006 s per swing.
Why does the measured period not match the formula at large angles?
The formula assumes sin θ ≈ θ, which is only true for small angles. At 90° the real period is about 18% longer than the formula gives, and near 180° it grows without limit as the bob almost balances at the top.
How does the simulation move the pendulum?
It solves the equation of motion θ″ = −(g ÷ L) sin θ − c θ′ numerically, in small time steps, so it is exact for any angle, and the period is measured from the times the bob passes the bottom.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.