HELP Does anyone know anything about elliptical motions of Pendulums?

[aw7879]

HELP! Does anyone know anything about elliptical motions of Pendulums?

I'm carrying out a research project on the Foucault Pendulum, and obviously a major issue with one of these devices is the precession caused by elliptical motion. I don't understand why elliptical motion, once present becomes more pronounced over time. Can anyone help?

 

[Cleonis]

I'm carrying out a research project on the Foucault Pendulum, and obviously a major issue with one of these devices is the precession caused by elliptical motion. I don't understand why elliptical motion, once present becomes more pronounced over time. Can anyone help?

Let's say a particular Foucault setup has a suspension that is not symmetrical enough; the wire bends slightly more easily in one direction than in another. The ease of bending affects the period.
So there will be one particular direction of swing with the largest natural period of swing, and perpendicular to that the direction of smallest period of swing. Let's say that it so happens that when the pendulum is started the direction of swing is precisely halfway those two.

You can think of the overall swing as a linear composition of two perpendicular harmonic oscillations that are in phase with each other. That is the crucial bit; when the swing is started the two composing oscillations are in phase with each other.

But in the case of a bias in the suspension the two oscillations do not remain in phase. Eventually the two oscillations will be 90 degrees out of phase, and the pendulum bob is moving in a circle.

If the pendulum swing is started perfectly the initial swing is along a single line, but as a phase difference starts to build up the swing opens up into an ellipse.


The scenario that you describe, I don't think that can occur. What you describe sounds like a runaway effect; a suggestion that a swing, once perturbed, will deteriorate more and more. That's not how I understand it. If the biased pendulum is allowed to keep swinging then at some point in time the composing harmonic oscillations will be in phase again. But of course a setup that behaves like that is useless as a Foucault setup.

 

[Borek]

http://en.wikipedia.org/wiki/Lissajous_curve

(with a=b).

 

[aw7879]

Thank you very much, that makes perfect sense.

Can anyone point me in the direction of any interesting diagrams showing precession caused by an elliptical pendulum?