Following Dynamically Defined Dancing Pendulums, another three versions of the dancing pendulum theme.  First a POV-RAY version by PM 2Ring, complete with reflections and shadows:

POV-Ray Pendulums (click to open in a new window)

and an interactive Javascript version:

Javascript pendulums by PM2Ring (click to view, or right click to download the javascript file).

Discussion and code for the javascript version can be found at the ABC (Australia) Tech-Talk Forum.  The pendulum code is spread over three forum posts (because of forum limitations on post length), but the complete HTML file can be downloaded by right clicking on the link above.  The Tech Talk discussion also has code for a very nice animated butterfly (also by PM 2Ring):

Javascript Butterfly

Fianally Hui, a regular guest contributor at Chandoo’s Pointy Haired Dilbert Blog, has done an in-Excel version, using a scatter (XY) chart.  This is where I started, but I wasn’t able to get a smooth animation.  The secret is to use named formulas for the pendulum positions, linked to the chart ranges.  Hui gives detailed descriptions of the procedure at two blogs:

The Excel Hero Blog gives detailed descriptions of the formulas for the pendulum motion, and how to link these to named formulas, and

Chandoo’s Pointy Haired Dilbert Blog gives more details about how to automate the process.  Both posts contain links to the Excel file with working animations and full open source code.