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Swing Pumping: Parametric Resonance Lab (2D)

A 2D theoretical-mechanics simulator: pump a playground swing by shortening and lengthening the pendulum's effective length and watch parametric resonance grow the amplitude from the governing equation theta'' + 2(L'/L)theta' + (g/L)sin(theta) + c*theta' = 0, tracked live on a swing view, a phase portrait, and a time strip.

Physics & Mechanics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

A playground swing is a rigid pendulum with one twist: the rider can change the distance from pivot to centre of mass at will, by standing up or crouching down. This simulator integrates the exact equation of motion for that time-varying-length pendulum in real time — θ̈ + 2(L̇/L)θ̇ + (g/L)sinθ + cθ̇ = 0 — and drives L(t) either the way a real swinger does (stand at the bottom, crouch at the extremes, automatically phase-locked to the motion) or with an explicit driving frequency you control, so you can see parametric resonance appear only near the 2:1 ratio and watch the nonlinearity cap the growth into a steady limit cycle. A side-view swing animation, a live phase portrait, and a scrolling time strip of θ(t)/L(t) all track the same integrated state.

⚙ Under the hood

A 2D theoretical-mechanics simulator of a playground swing as a pendulum with time-varying length: stand up or crouch (or drive it at a fixed frequency) and watch parametric resonance grow the swing's amplitude near the 2:1 drive ratio, tracked live on a swing view, a phase portrait, and a scrolling time strip, capped by nonlinear detuning into a steady limit cycle.

theoretical mechanicsparametric resonancependulumLagrangian mechanicsnonlinear dynamics2D canvas

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