Inspired by a video showing the seemingly chaotic movements of pendula of varying lengths, I created this animation in Geogebra.
Using sine functions of varying periods, I was able to create a set of points that oscillate in a manner similar to the pendula in the “Pendulum Waves” video.
Consider the point on the bottom as the timekeeper. In the the time it takes the bottom point to complete one full trip (from center to right to left back to center), the next point up completes two full trips; the point above that three full trips, and so on.
Since every point is completing a whole number of trips in that amount of time, they will all sync up every time the bottom point is ready to start again. And watch the “even” points to see when they sync up, too!
