Presets

2:1 Resonance

Gentle Swing

Stiff Spring

Chaotic

Parameters

Spring constant k: 40 N/m Mass m: 1.0 kg Natural length L₀: 1.0 m Gravity g: 9.81 m/s² Damping: 0.00 Initial angle θ₀: 30° Initial stretch: 0.0 m

Energy split

Elastic

Swing

Grav

Stats

Length r—

Angle θ—

Elastic E—

Pendular E—

Total E—

ω_spring / ω_pend—

Regime—

A bob hangs on a spring (radial coordinate r) and also swings (angle θ) — a 2-DOF coupled oscillator. The Lagrangian gives two coupled ODEs solved with RK4. When the spring frequency ≈ 2× the pendulum frequency, energy sloshes between bounce and swing (autoparametric 2:1 resonance).