Write expressions for the kinetic energy, the potential energy, & the Lagrangian of the system.

A plane triatomic molecule consists of equal masses m at the vertices of a triangle. If the masses were at rest, the masses would be on an equilateral triangle of side b. The molecule is held together by forces that are harmonic for small oscillations & the force constants are each equal to k. Consider motion in the plane of the molecule only.

Write expressions for the kinetic energy, the potential energy, & the Lagrangian of the system.

Derive the equations of motion using Lagrange’s equations.

Assume small oscillations. Set up & solve the solve the secular equation for the normal mode eigenfrequencies & eigenvectors. How many normal modes are there? Do any of them correspond to ω = 0?

Answer the following question using mostly WORDS, in complete, grammatically correct

English sentences! You may also make a sketch if that helps your discussion.

Qualitatively discuss the motion of the 3 masses in each of the normal modes.

 

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