(a) In the linear triatomic molecule, suppose the initial condition is that the center atom is at rest but displaced by an amount a0 from equilibrium, the other two being at their equilibrium points. Find the amplitudes of the longitudinal small oscillations about the center of mass. Give the amplitudes of the normal modes.
(b) Repeat part (a) but with the center atom initially at its equilibrium position but with an initial speed v0.
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