PPolySim OS

Pendulum Wave

A row of pendulums, each a touch longer than the last. As their periods drift apart they paint traveling waves — then snap back into perfect sync.

Pendulum WaveLive

Controls

A row of pendulums with slightly different lengths. They drift in and out of phase, weaving traveling waves, then briefly snap back into sync.

Presets

▶ Run in Python

Data Inspector

Pendulums18
Slowest period2.00 s
Fastest period0.61 s
Effectphase waves

Governing equation

Reading this result: Each of the 18 pendulums is set to a slightly different length, so its period drifts from the slowest (~2.00s, 30 swings per cycle) to the fastest (~0.61s, 98 swings per cycle). With a period spread of 4, the phases fan out into a traveling wave, dissolve into a chaos-looking scramble, and then all re-sync at the common 60-unit cycle before repeating. Wider spread reaches the disordered stage sooner; more pendulums makes the wave smoother.

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How it works

Each pendulum has a slightly different length and therefore period. Starting in phase, they gradually separate, producing snake-like traveling and standing patterns, before realigning after a full cycle — a beautiful demonstration of phase and frequency.

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Frequently asked questions

Is this pendulum wave tool really free?▾
Yes. Pendulum Wave runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.