Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Mr Andrew on 05/09/2007 23:30:25
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What exactly is a duffing oscillator? I've seen several versions and one is obviously chaotic (not sure why though...I just saw the graph) and the other is periodic. Why is the one chaotic? Help PLEASE!!! [???] [???] [???]
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It is much to complex for me to either understand or explain but but 'Google' has quite a lot to say about Mr Duffing's ideas, it seems that a resonant system with a non linear restoring force when driven slightly off frequency behaves with low drive but becomes chaotic when overdriven.
I seem to recall seeing this happen in some equipment but cannot recall exactly which.
PS it was an early electric watch that had both a balance wheel and a Xtal.
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Looking at the google references it look similar to those executibe toys where you have a magnetic pendulum swinging over several magnets that can be adjusted to attract it or repel it. if you group the magnets quite close together and start the pendulum swinging vigorously initially it will look like it is swinging quite normally because the energy in the swing is much larger than the affects of the magnetic forces but as the swing dies down the forces exerted by the magnets get more significant and the pendulum starts to swing around wildly with divverent frequencies.
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That description is one of the two I've heard...the other one is of a metal bar vibrating by being attracted to an electromagnet and then repelled--but that is not chaotic. Why is the first chaotic? I can't seem to reason it out.
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There are several attractors and/or repellers this means that there are several saddle points in the system where it is possible for the direction of the swing to be very finely balanced against two possibilities with entirely differen outcomes. If you watched one of thesr pendulums swinging you would bein very little doubt about its chaotic and unpredictable pattern I have one on my desk at the moment.