Driven Resonance

Drive an oscillator near its natural frequency and the amplitude explodes. Lower the damping and the resonance peak grows taller and sharper — the physics behind everything from radios to collapsing bridges.

Driven ResonanceLive

amplitude near the natural frequency

Controls

Presets

Natural frequency f₀ (Hz)

Damping ratio ζ

Drive frequency (Hz)

Push a swing at its natural frequency and the amplitude blows up — resonance. Less damping → a taller, sharper peak (higher Q). This is why bridges, buildings, and wine glasses each have a frequency you must avoid.

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Data Inspector

Response amplitude8.44e-2

Quality factor Q3.3

At resonance?yes ≈ peak

Governing equation

A (ω) = \frac{F _{0}}{( ω _{0}^{2} - ω ^{2} ) ^{2} + ( γ ω ) ^{2}}, ω = 2 π (1.00), ζ = 0.15, A = 8.44 e - 2

Reading this result: Driving at the natural frequency f₀, so you sit on the resonance peak; the damping ratio ζ caps the height at a quality factor Q of 3.3.

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How it works

A damped driven oscillator has steady-state amplitude A(ω) = F/m ÷ √((ω₀²−ω²)² + (γω)²), which peaks near the natural frequency ω₀. The sharpness of the peak is the quality factor Q = 1/(2ζ). This resonance is exploited in tuning circuits and avoided in structural design. Educational tool.

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Frequently asked questions

Is this driven damped resonance curve tool really free?▾

Yes. Driven Resonance 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.