Twinnel

Meet Twinnel, two brass pendulums joined by a spring who keep passing their swing to each other.

Hang two identical pendulums side by side and link them with a weak spring. Pull one aside and let go. At first only that one swings. Slowly its motion fades while the other starts swinging, until the first is almost still. Then the energy flows back again.

This exchange happens because the pair has two natural patterns, called normal modes. In the first they swing together and the spring never stretches, so ω₁ = √(g/L). In the second they swing opposite and the spring adds a pull, so ω₂ = √(g/L + 2k/m).

Starting one pendulum mixes both modes. Their slightly different frequencies beat against each other, and the energy swaps over with the beat period 2π/(ω₂ − ω₁). For 1.0 m strings, 0.50 kg bobs and a 0.10 N/m spring, ω₁ ≈ 3.13 rad/s, ω₂ ≈ 3.20 rad/s, and the beat period is about 100 s.

Normal modes explain how vibrations travel through crystals, how molecules vibrate, and why two pendulum clocks on the same wall can end up ticking in step.