Chaotic Pendulum

A chaotic pendulum can be constructed in various different ways. Here we present designs of three different types we have used. The basic idea is to produce a pendulum that never repeats itself. It could be said that the period of the motion is longer than the age of the universe, and the system is chaotic.

Motorised Chaotic Pendulum

In the motorised chaotic pendulum, a bar magnet is suspended at its middle from a string so that it can move in any direction. If such a device is given a known initial displacement from equilibrium then the resulting motion should be completely predictable.

In order to introduce a non-deterministic factor, we can set a second bar magnet spinning just underneath the suspended magnet. Then, when the suspended magnet passes equilibrium, it experiences a force from the spinning magnet and the interaction sends the suspended magnet off on a completely unpredictable path. In our exhibit, we have hidden the second magnet under a wooden base and used a motor to rotate it so that viewers can be quizzed on what they think is going on.

Passive Chaotic Pendulum

An even simpler design of pendulum than that above is to place four or five small permanent magnets on the base just underneath the suspended magnet. 

When the suspended magnet is given its initial displacement, the interaction with the fixed magnets is crucially dependent on the initial conditions, and chaotic motion is again observed, although this time the motion eventually stops, and the final position of the pendulum is ultimately determinable.

Roch's Pendulum

This is a particularly curious mechanical system where a number of compound strips are connected together with bearings to form a sort of star shaped pendulum. When the system is given a rotation, the subsequent transfer and exchanges of energy to and from various parts of the system is extremely sensitive to the initial spin. 

The pendulum is best mounted on a very heavy frame so that energy lost to the surroundings is minimised. Even when the system looks as if the motion is dying away, it can simply be as a result of the various spurs rotating in the same direction so as to make the structure appear as a rigid body with large moment of inertia. When the spurs begin moving differently, the energy conservation causes the smaller satellite systems to spin up, making it appear to the casual observer as if the system is gaining energy from nowhere!