(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Problem: Derive eigenvalue equation of motion of a system undergoing free small oscillation in three dimensional space.

2. Relevant equations

3. The attempt at a solution

I want to know if I have correctly written the values of T and V---

[tex]\ T=[/tex][tex]\frac{1}{2}[/tex][tex]\ m [/tex] [[tex]\dot{x}^2 +\dot{y}^2+ \dot{z}^2[/tex]]

And [tex]\ V=[/tex][tex]\frac{1}{2}[/tex][tex]\ k [/tex][[tex]\ x^2+\ y^2+\ z^2 [/tex]]

I m not sure if I have written the write thing...what should be the sign of k.Should I write -ve?And is it OK to assume that the force constants are equal?What would be if they were not equal?Would they simply add like (1/2)(k1+k2) x^2?

If I can form T and V,I am confident that I will be able to do the rest of calculations.

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# Homework Help: Classical Mechanics problem

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