4. Consider a diatomic molecule AB with masses mA =m, mg = 2m. Let the equilibrium distance between the two atoms be a, find center-of-mass coordinates of the molecule.

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4. Consider a diatomic molecule AB with masses ma =m, mg =2m. Let the equilibrium distance
between the two atoms be a, find center-of-mass coordinates of the molecule.
Assuming that the potential energy of the molecule can be approximated by V(r,, r2) =
5(Iri - r2|- a), where ri and r2 denote particle positions at time t, set-up the matrix equation to
compute the normal modes of vibration. Compute the normal mode (correct linear combination)
and the frequencies.
Transcribed Image Text:4. Consider a diatomic molecule AB with masses ma =m, mg =2m. Let the equilibrium distance between the two atoms be a, find center-of-mass coordinates of the molecule. Assuming that the potential energy of the molecule can be approximated by V(r,, r2) = 5(Iri - r2|- a), where ri and r2 denote particle positions at time t, set-up the matrix equation to compute the normal modes of vibration. Compute the normal mode (correct linear combination) and the frequencies.
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