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Driven Resonance: Forced Oscillator (2D)

2D mass-spring-damper lab: RK4-integrated equation of motion, a live displacement/force trace and a resonance curve A(ω) with a marker showing exactly where the driving frequency sits relative to ω0.

Physics & Mechanics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion numerically integrates the same driven mass-spring-damper equation as the 3D version — F0·cos(ωt) pushing a mass through a spring and a damper — and renders it as a plain animated oscillator plus two live plots: a displacement/force trace over time and a resonance curve A(ω) with a marker showing exactly where the current driving frequency sits relative to the natural frequency ω0, so the amplitude blow-up near resonance and its dependence on damping are both directly visible.

⚙ Under the hood

2D mass-spring-damper lab with RK4-integrated equation of motion, a live displacement/force trace, and a resonance curve A(ω) with a marker so amplitude blow-up near ω0 is directly visible.

resonanceforced oscillationsharmonic oscillatordampingquality factorrk4

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install

FAQ

Why does the amplitude peak below the natural frequency, not exactly at it?

Damping shifts the amplitude peak slightly below ω0 for any driven damped oscillator; only in the undamped limit does the peak sit exactly at ω0. The resonance curve panel shows this shift directly as you change the damping slider.

What does the quality factor Q tell you?

Q = ω0 / (b/m) measures how sharp the resonance peak is: a high-Q system (light damping) rings for a long time and has a narrow, tall peak, while a low-Q system settles quickly and barely shows a peak at all.