Contingency, Chaos and A Couple of Pendulums

Notes

Every oscillation of the pendulum is represented by one cycle around this ellipse, and every time, the motion gets closer and closer to being simply on the ellipse. Another way of looking at the data is by looking at one sample every four seconds (the period of the driving force) - in that view, the motion of the pendulum is described by one point per cycle - and that point rapidly moves until it is on the ellipse.

One person in the audience confused this ellipse with the possibility of elliptical motion of the pendulum (swinging left/right as well as back/forth) - that's a different issue (and unless the driving force is in two dimensions, that kind of elliptical motion will damp out quickly).

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