Please, this is something I have thought of a long time, but don't have unlimited supplies to keep doing it wrong. I want to make one of these for my nephew, he's interested in science!
There is a Physics Toy, called "Swinging Sticks", used in the movie "Iron Man 2", on Pepper Pott's desk. How can I calculate the 2 balance points for the "sticks" in this toy, to make it keep spinning a long time? - Here is a great Youtube video of the toy:
I'm really brainless when it comes to calculating, but I think this can be determined easily without any calculation. Let's call the bar attached to the fixed stand the "primary bar", the other one the "secondary bar".
The balancing point on the secondary bar is slightly offset from the secondary's center (gravity) point. As a ballpark figure, I would assume that an offset of $\frac{1}{20}$th of the secondary's length should do. This causes the secondary to always assume the upright position when in rest. This point is attached to the primary bar somewhere close to its end.
The balancing point of the primary again is offset slightly from its gravity center point, only this time the secondary's mass is part of the account. I would try to find the primary's center of mass by balancing it horizontally while the secondary dangles down from its end. When the sweet spot is found, shift it $\frac{1}{20}$th of the primary's length towards the secondary bar. This will be the pivot point for the primary on the stand, causing the long end of the primary to outweigh its short end plus the secondary.
As a rule of thumb, it can be assumed that the larger the offsets, the more rapid the sticks will act. Smaller offsets will result in calmer movements. It might be an interesting project to build a model with variable pivot points to experiment with.
