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I'm taking a course on mechanical vibrational analysis and this is what I was told by my professor, but I'm curious if there are any counter-examples.

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Consider a particle moving in an $|r|^2$ potential. One possibility is circular motion, which can be viewed as harmonic "vibrations" in orthogonal directions, $\pi /2$ out of phase. Now consider a particle moving in an $|r|^{-1}$ potential. Circular motion is also possible, but is it a "vibration"?

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  • $\begingroup$ There's no exchange of energy in circular motion. I'm curious about vibrations that involve energy exchange, and if there is any type of vibration where energy is exchanged in other forms than kinetic <-> potential. $\endgroup$ – Cedric Eveleigh Mar 12 '16 at 23:44
  • $\begingroup$ In electromagnetic waves or LC circuits, energy is exchanged between electric and magnetic fields. This might not meet your definition of "mechanical". $\endgroup$ – Keith McClary Mar 13 '16 at 5:12
  • $\begingroup$ Is that an exchange between two different forms of potential energy? $\endgroup$ – Cedric Eveleigh Mar 13 '16 at 21:55
  • $\begingroup$ A different way of looking at it is that current in an inductive circuit is analogous to momentum. Sorry, I don't think there is a clear cut answer for this. It depends on how you define your terms and your interpretation. $\endgroup$ – Keith McClary Mar 14 '16 at 3:11
  • $\begingroup$ If we use electromagnetic radiation as an example, is the exchange of electric and magnetic energy an exchange of two forms of potential energy? $\endgroup$ – Cedric Eveleigh Mar 15 '16 at 15:25

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