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Swing Pumping: Parametric Resonance Lab

A 3D 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) = 0.

Physics & Mechanics3DAdvanced60 FPS📱 Mobile-adapted⇄ 2D 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.

⚙ Under the hood

A 3D 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, capped by nonlinear detuning into a steady limit cycle.

theoretical mechanicsparametric resonancependulumLagrangian mechanicsnonlinear dynamicsthree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install