How do I simulate a bouncing ball?

Open this page and use the live Coupled Oscillators tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a bouncing ball from your own measurements.

Use case · powered by Coupled Oscillators

Coupled Oscillators for a bouncing ball

Simulate a bouncing ball live in your browser. This runs the real Coupled Oscillators solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

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Coupled OscillatorsLive

normal modes & beating

Controls

Presets

Outer spring k (N/m)

Coupling spring (N/m)

Mass (kg)

Two masses linked by a spring exchange energy. Any motion is a mix of two normal modes: in-phase (slow) and out-of-phase (fast). Their beat produces the sloshing you see.

▶ Run in Python

Data Inspector

Mode 1 (in-phase)0.712 Hz

Mode 2 (out-of-phase)0.955 Hz

Beat frequency0.243 Hz

Governing equation

ω_{1} = \frac{k}{m} = 4.47, ω_{2} = \frac{k + 2 k _{c}}{m} = 6.00 rad/s (k = 20, k_{c} = 8, m = 1)

Reading this result: The beat frequency is set by the coupling: at kc=8 versus k=20, energy fully sloshes from one mass to the other every 2.1 s, and stiffer coupling speeds that exchange up.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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About this simulation

The full Coupled Oscillators tool models a bouncing ball with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

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Other ways to simulate a bouncing ball

Particle / N-Body for a bouncing ball Heat & Wave Fields for a bouncing ball GPU Compute (WebGPU) for a bouncing ball WebGPU Fluid for a bouncing ball GPU N-Body for a bouncing ball GPU PDE Solver for a bouncing ball

Frequently asked questions

How do I simulate a bouncing ball?: Open this page and use the live Coupled Oscillators tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a bouncing ball from your own measurements.