Where it shows up
This two-frequencies-from-one-coupling story is everywhere. It is why two slightly detuned guitar strings produce an audible wobble, why pushing a child on a swing in time with a neighbouring swing can pump energy across, and — in the quantum version — why a particle tunnels between two nearby wells, splitting a single level into a symmetric and antisymmetric pair. The same algebra governs molecular vibrations, coupled LC circuits, and avoided crossings in band structure. The lesson is general: couple two identical resonators and their degenerate frequency splits in two, and any localised excitation must beat between them.
The knobs
- Initial condition — choose Left displaced (excites both modes, full beating), Both displaced, or the pure Normal mode 1 (in phase) and Normal mode 2 (out of phase), which oscillate steadily with no energy transfer.
- Coupling k_c — strength of the connecting spring. More coupling widens the mode split and shortens the beat period.
- Speed — time-scale of the simulation; rescales how fast the whole dance plays out.