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CLASSICAL MECHANICS / LAB 04

Coupled pendulums & energy transfer

Displace one oscillator and watch its energy migrate through an adjustable coupling into the other.

1 — ORANGE · 2 — CYANREADY
Time 0.00 sMode MixedFlow Balanced

Oscillation diagnostics

Oscillator 1 energy0 J0%
Oscillator 2 energy0 J0%
Coupling energy0 Jtorsional spring
Total energy0 Jloss 0%
Predicted transfer—small-angle estimate
WHAT YOU ARE SEEING

Energy moves even when the pendulums do not.

Coupling

The torsional spring responds to the angle difference. It removes energy from one oscillator while doing work on the other.

Normal modes

In-phase and out-of-phase patterns are the system’s natural collective motions. General motion is a mixture of both.

Beating and detuning

Nearby normal-mode frequencies create a slow energy envelope. Different lengths reduce the completeness of transfer.

ω₊ = √(g/L) · ω₋ = √(g/L + 2κ/mL²) · Ttransfer ≈ π/|ω₋−ω₊|