Brady Romberg's Compact Pendulum

In this setup there are two inverted pendulums with T-shaped rod extending between them.  The mass at the lower end of the "T" will move in a very slight arc, simulating a very long pendulum.  The dimensions of this pendulum are:

15 cm-long pendulums
30 cm between pendulums bases
10 cm connecting rod
10 cm vertical rod with mass at lower end

I wrote a FORTRAN program to compute dimensions that would work for this design.  By trial and error I came up with the dimensions indicated above (the diagram is not to scale).  Some of the points generated by the program are graphed below using MS Excel.  The arcs below show the upper end of the vertical rod and points 5, 10, and 15 cm along it.  Note that the upper end is concave downward, as is the point at 5 cm.  The points at 10 and 15 cm are concave upward.

I've build a pendulum based on this design, which is described here.