Pendulum Wave

I became fascinated with the math behind the pendulum wave and wanted to create one that would oscillate for at least a minute. My pendulum wave uses 11 pendulums ranging from 140mm to 300mm in length with a 24 second oscillation period. I used a piece of 1.75mm filament to hang the pendulums for minimum friction and maximum oscillation time. Here's a high quality video (the GIF is kind of jerky). The lengths of the pendulums are set such that in a given time t, the first pendulum completes x oscillations, and each subsequent one completes one more oscillation than the previous. As all pendulums are started together, their relative phases change continuously, but after time t, they come back in sync and the sequence repeats. This is the formula for pendulum length:Where:L= length of the pendulumT= oscillation periodg= gravitational accelerationk= is a constant determined by the first pendulum in the seriesn= pendulum number I created a spreadsheet to determine the length of each pe