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!

*Click here to see more in Technology.*

Wow, its cool how if you look all the points at the same time. You will see the points moving as if they are moving in a 3D space. Sometime its look like a moving vortex; sometime it looks like a rotating parabola. It is cool how things moving in a plane, can create a 3D feeling

For some reason this reminded me of this. http://www.youtube.com/watch?v=hlx-M53dC7M&NR=1 In Germany, the BMW museum has this displayed. Not so much of a pendulum, but it seemed to me that these kinetic balls showed various 3D planes and curves (some of the equations used in multi-variable calculus). Thought you might be interested in taking a look at it too.

This reminded me of http://www.youtube.com/watch?v=dLhNdmZ7lDw. Not so much of a pendulum, but the whole ball theme seemed to fit in. For me the bmw kinetic balls reminded me the various equations for curves and planes in 3D (multi-varible calculus). Thought you might be interested in taking a look at it too.

Sorry for the double post. My first commented didn’t show at first so I posted it up again.

Wow! Thanks for sharing, Brian–that is awesome! At first I thought it was a magnetic sculpture, but the balls are on individual strings. Very cool!