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Here is a further refinement of the model for Mike Meyers' kinetic sculpture in Lyon.

Assumed:
Bottom is turned 3π radians - 1.5 turns.
When turned π or more radians either way, the restoring force is a constant.
Damping is directly proportional to the angular velocity. This assumption makes sense for the untwisted mode, but I think that damping might not be the same when the center is twisted.

The plots on the right are of angle and height of the bottom ring as functions of time. For the angle, the red lines are ±π, which separate the twisted and untwisted states.

Created by Mathematica  (February 5, 2006)