A triatomic molecule like hydrogen sulfide (H2S) consists of two hydrogen atoms of mass m...

A triatomic molecule like hydrogen sulfide (H2S) consists of two hydrogen atoms of mass m and one sulfur atom of mass M constrained by atomic bonding forces to assume the tri­angular configuration shown in Figure. Assume that the bonding forces can be approximated by springs whose force constant is k. When the three atoms are in their equi­librium configuration, the HS distance is a = 1.67 × 10–10 m and the H–S–H vertex angle is approximately 2α = 90°. Find the normal frequencies and normal modes of oscil­lation. Assume that the hydrogen atoms do not interact directly with each other.

Figure