This is a project that uses an electronic magnetic pendulum drive similiar to instructables: http://www.instructables.com/id/The-Magbot-pendulum/
although the circuit I actually use is found here: http://www.trainelectronics.com/Pendulum/article.htm
I orginally built this pendulum circuit to work on a Foucault Pendulum which I have partially working but decided to use the pendulum drive to make this video of a double and an unbalanced pendulum.
The unbalanced pendulum is kind of interesting; there is only a certain amount of weight you can add to the top of the pendulum before it becomes disfunctional. Also you find that the heavier the little pendulum at the top, the less efficient the pendulum at the bottom. By adding a smaller pendulum to the top of the main pendulum you find the swing of the main pendulum getting reduced a bit. Not sure what is going on there.
Please watch the video to see how it works.
I haven't found any research so far that deals with double pendulums built the way this particular one has been built. I think this pendulum would be a great science fair project as it is somewhat unique. Also there seems to be no studies on this particular unbalanced pendulum as well.
I keep this pendulum in my living room and sometimes let it run for days as the batteries last forever and the pendulum makes a pleasant sound. It is also relaxing to just sit and watch it work.