A plane triatomic molecule consists of equal masses m at the vertices of an equilateral
triangle of sides a. Conﬁne the system to 2 dimensions, and write the Lagrangian,
assuming that the atoms interact with each other via a potential U that only dependes
on the interatomic distances. How many modes of oscillation are there? In the small
oscillation approximation, taking the force constant of all interations to be equal to k,
ﬁnd the frequencies of oscillation of the molecule.

Question

A plane triatomic molecule consists of equal masses m at the vertices of an equilateral
triangle of sides a. Conﬁne the system to 2 dimensions, and write the Lagrangian,
assuming that the atoms interact with each other via a potential U that only dependes
on the interatomic distances. How many modes of oscillation are there? In the small
oscillation approximation, taking the force constant of all interations to be equal to k,
ﬁnd the frequencies of oscillation of the molecule.