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Re: [Phys-l] question about coupled oscillators



Having thought about it a little more, this is what I come up with:

Newton's third law says that oscillators i and j exert equal magnitude forces on each other. This in turn will lead to elements K_ij and K_ji in the force-constant matrix K to be equal. In turn, this means K is symmetric (and of course it's real); and so is the mass matrix M. But this means the eigenvectors must be real, even if I write the oscillator displacement vector x in complex form where the i-th component is A_i exp (i d_i). But this means d_i can only be 0 or pi.

What do you think of this argument? -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/