Sympathetic Resonance: Rigorous Analysis & References

[PhilDSP]

Does anyone have any references to a rigorous analysis of sympathetic resonance?

I'd imagine that the transfer of momentum occurs not through interacting waves, which would indicate an exception to the superposition principle, but because of cross effects of both waves affecting the absorbing objects. I'm curious also if gravity tidal effects (such as the moon being pushed away from the Earth due to a transfer of angular momentum) are closely related to sympathetic resonance.

 

[Simon Bridge]

In physics they are just resonance effects.

Tide-locking is an example of a resonance effect in gravity - but you can also see it in a driven harmonic oscillator. The sympathetic resonance examples are all forms of some oscillating source driving another oscillator. With tuning forks for eg. one fork vibrates the air, and the air pushes and pulls on the other one ... if conditions are right, the second one starts vibrating.

Or are you thinking of something else?

 

[sophiecentaur]

You may have some joy if you search with "coupled resonators" or "coupled oscillators".

 

[Andy Resnick]

Does anyone have any references to a rigorous analysis of sympathetic resonance?

Another context comes from certain stringed instruments:

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

http://perso.univ-lemans.fr/~jgilbert/ArticlesPageWeb/2005_LeCarrou&al_Acustica_ModellingOfSympatheticStringVibrations.pdf
http://www.google.com/url?sa=t&rct=...9tTvAw&usg=AFQjCNHxCyP_QCgxWoaW_VwjL4nZMHqwXQ
http://www.gearwire.com/nord-stagepiano-wnamm2010.html

 

[PhilDSP]

Thanks for the interesting ideas and links