Pendulum i (0-indexed) completes N + i full oscillations during one realignment period T, so its own period is Ti = T / (N + i). Every pendulum starts in phase at t = 0. Because each one is slightly faster than its neighbour, they drift out of phase, sweep through travelling-wave, standing-wave and "chaotic" looking patterns, and then all land back in phase exactly T seconds later — a direct demonstration of superposition of the individual sinusoidal motions.
- Angle of pendulum i: θi(t) = θmax · cos(2π t / Ti)
- Bob position: xi + Li·sin(θi), ypivot + Li·cos(θi)
- Small-angle pendulums with equal length would need different gravity per pendulum; instead each string length here is tuned to the target period at fixed g, which is the same trick the physical desktop toy uses.