Link two oscillators with a spring and energy sloshes back and forth between them. That motion is just two hidden normal modes beating against each other.
Coupled OscillatorsLive
normal modes & beating
Controls
Presets
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.
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.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
Two masses joined by springs have two normal modes: an in-phase mode at √(k/m) and an out-of-phase mode at √((k+2k_c)/m). Any starting motion is a superposition of the two, and their slightly different frequencies produce the characteristic energy-exchange beat. Educational tool.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this coupled oscillators normal modes tool really free?▾
Yes. Coupled Oscillators 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.