The principles of resonance are such that the greatest amplitude of a vibrational or electrical wave peak at a certain frequency, and they peak while consuming less power overall to maintain it.
I'm wondering, since an electron has a resonant frequency, and so does a system of water molecules, brick, person, and planet; how would an incoming vibrational wave of infinite 'Q' (so basically it has a very accurate and narrow bandwidth resonant frequency) tell the difference between two objects of the same resonant frequency?
So if you have an apple that resonates at 10.8Hz, and an apple that resonates at 10.3Hz, and your incoming wave is at 10.8Hz with infinite Q, obviously all of the power goes to the first apple, and it peaks.
But if you have an 11Hz apple and an 11Hz pear, (two different objects), what happens?
I would think that if you had two identical apples at 11Hz, it would split the power between them such that the new amplitude is some lesser exponential than it would have been if there was only one apple at 11Hz.
What if the wave is not vibrational, but electromagnetic, same thing right?
Best Answer
As a general rule, two "degenerate" oscillators (i.e. two oscillators with the same frequency) will no longer have the same frequency if they interact with each other, however weakly; the degeneracy is usually broken. So if you have two identical resonators with a fundamental of 11 Hz, and you bring them together, the combined system will have resonant frequencies of something like 11.001 Hz and 10.999 Hz. Exactly how big the shift is will depend on how strong the resonators are "coupled" with each other, and it may be imperceptibly small depending on the limits of your measurement.
This general phenomenon, of degeneracy breaking, is pretty independent of the exact details of the system or the precise form that the energy takes in its "kinetic" and "potential" forms (or how energy is transferred between the systems.)