Julia Sets and the Mandelbrot Set

Basins of Attraction of Mechanical Systems

All mechanical systems include some amount of friction. We say the pendulum is damped.

Regardless of the starting position or speed of the pendulum, eventually it will come to rest over one of the magnets.

There are two exceptions: if the pendulum is straight down and at rest, or straight up and at rest, it will stay there.

Are these stable or unstable? This depends on how strong the magnets are compared with gravity, and on the amount of friction.

From which starting positions and speeds will the pendulum come to rest over the left magnet? From which will the pendulum come to rest over the right magnet? This is the question we want to answer.

Return to Mechanical Basin Boundaries.