Home▸Physics & Mechanics▸Small vs Large Angle Pendulum Comparator

🔴 The Pendulum: Small-Angle Lie vs the Real Nonlinear Swing

Interactive 3D pendulum where increasing the swing amplitude shows the period diverging from the small-angle approximation, comparing simple harmonic motion against the true nonlinear solution.

Physics & Mechanics3DModerate60 FPS

Two pendulums released together from the same amplitude: one integrated exactly from the nonlinear equation of motion, one following the textbook small-angle formula. Watch them fall out of sync as amplitude grows.

🔬 What It Demonstrates

The small-angle approximation sin θ ≈ θ underestimates the restoring force at wide swings, so the real pendulum's period is always longer than T₀ = 2π√(L/g) predicts — and the gap grows nonlinearly with amplitude.

🎮 How to Use

Drag the amplitude slider from a few degrees toward 170° and watch the red pendulum drift behind its pale ghost. Change length or gravity to rescale the timescale, and compare the live period and phase-drift readouts.

💡 Did You Know?

At 90° amplitude the true period is already about 18% longer than the small-angle formula; the period diverges to infinity as the release angle approaches 180°.

⚙ Under the hood

Interactive 3D pendulum where cranking the swing amplitude past small-angle limits shows how the true nonlinear period diverges from the textbook approximation.

pendulumsmall-angle-approximationnonlinear-dynamicsperiod-of-oscillationclassical-mechanicsphysics

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