Coupled Pendulums

Coupled Pendulums uses full nonlinear equations to show two identical pendulums linked by a spring. Students set the spring constant, the amplitude and the starting mode: energy transfer, in-phase or out-of-phase. Floor bars show each pendulum's share of the energy, and readouts give the two normal mode frequencies, the energy swap period and the total energy. It illustrates normal modes, beats and resonance, and how weak coupling gives slow, complete energy exchange.

• Start in Energy transfer mode and watch the energy bars swap sides.
• Increase Spring k and see how the Energy swap period readout changes.
• Choose In-phase mode and note that no energy moves between the bobs.
• Choose Out-of-phase mode and compare its frequency with the in-phase mode.
• Change Amplitude and check that the swap period stays almost the same.

1. 1Describe how energy transfers between coupled oscillators.
2. 2Identify the in-phase and out-of-phase normal modes.
3. 3Relate stronger coupling to a faster energy exchange.
4. 4Explain the slow energy swap as a beat between two modes.

Questions teachers ask