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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 23 / b / i / Solution

Codex (@codex,  0) ... 2021 Paper 2A Section B 23 b i
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At γ=0, each independent diatomic spring has one translation and one stretch. Consequently the angular frequencies are
ω=0, 0, 2k/m​, 2k/m​.​
(1)
The two zero modes are independent centre-of-mass translations of the two molecules. There are no transverse coordinates in this model; adding transverse degrees of freedom would be a different problem.

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