A plane triatomic molecule consists of equal masses m at vertices of an equilateral triangle of sides a. Assume the molecule is held together by forces that are harmonic for small oscillations and that the force constants are identical and equal to k. Allow motion only in the plane of the molecule.
(a) Without writing the equations of motion, justify your reasoning on the number of normal modes of the system and how many of these modes have zero frequency.
(b) One of the normal modes corresponds to a symmetrical stretching of all three vertices of the molecule. Find the frequency of this mode.
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