# Coupled oscillators - mode and mode co-ordinates

1. Apr 19, 2010

### joriarty

For this question I'm not going to introduce the particular problem I am working on, rather, I am merely wanting some explanation of a concept which I can't seem to find in any of my textbooks. I suspect the authors think it is just too obvious to bother explaining .

I'm revising for a test and have the full worked solutions for this problem in front of me. I can follow the mathematics, but not the reasoning behind it.

The question:

My worked solutions now say:

My question:

What exactly are q1 and q2, and why should these be equal to $$\sqrt{\frac{m}{2}}\left( \psi_{2}+\psi_{1} \right)$$ etc? Why $$\sqrt{\frac{m}{2}}$$? Is there a more specific name for this law that I could look up?

I hope my question is easily understandable! Thank you for your help.

(note: for the sets of equations relating q1 and q2 to m and x, there should be a "≡" sign rather than an "=" sign - for some reason my TEX formatting comes out with "8801;" rather than a "≡" sign. Odd.)

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Last edited: Apr 19, 2010
2. Apr 19, 2010

### joriarty

Formulae now fixed. I hope. Sorry if I confused anyone while I was editing things