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[Phys-l] question about coupled oscillators



In writing down the assumed form for the displacement of each oscillator i in a coupled system, in general one includes a phase constant d_i in the argument of the cosine:

x_i (t) = A_i cos (w*t + d_i)

However, in all the examples I can think of, the relative phases of the oscillators *in a single normal mode* always turn out to be either 0 or pi. Why can't we get other values?

In particular, the "weak coupling" problem (where you pull just one oscillator aside and then get beats) looks like an example of pi/2 relative phase difference between the two oscillators. Except I don't have a single normal mode; I have two normal modes equally excited. But there's a part of me that wants to call this something like another normal mode since each particle is oscillating in a nicely repetitive manner. (Okay, maybe I need to require the two normal mode frequencies to be commensurate for this statement to be exactly correct.) That is, I'm wanting to define "normal mode" as any smoothly repetitive pattern, but apparently that's too loose a definition to be right.

Please help clarify my thinking. -Carl
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-5002
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/