Question Bank MCQ • 1 Mark Section 2: Classical Mechanics Small oscillations

QB_PH_056: Small oscillations

Question Statement

A system with $N$ independent generalized coordinates oscillating about stable equilibrium has how many normal frequencies?
(A) N
(B) 2N
(C) N^2
(D) N!
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: The secular determinant $\det(\mathbf{V} - \omega^2 \mathbf{T}) = 0$ is a polynomial of degree $N$ in $\omega^2$.
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