Here’s a pendulum demonstration that was part of an Exploratorium exhibit in the atrium of the Hyatt where I was attending a frequency & timing conference this past week. The bobs all start off in phase but since the period (or frequency) of a pendulum depends on \(sqrt{L} \) (or its inverse), the relative phases rapidly diverge. The bobs occasionally hit a condition that looks less chaotic, such as the slightly-out-of-phase S shape, and the condition where alternate bobs are 180º out of phase. They then go back to the “S” before briefly all being in phase again. That occurs when they have all undergone an integral number of oscillations, with each one having undergone one more cycle as its neighbor as you move from the front to the back (long to short)

Here’s another video, via @JenLucPiquant with even more bobs.