As in Problem 9, consider a planar system of three identical masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of masses.

Use the character table in Problem 9 and use the coordinate displacements as the basis for a reducible representation.

(a) Express the reducible representation for the trivial zero-frequency normal mode translations as a sum of irreducible representations.

(b) Express the reducible representation for the trivial zero-frequency normal mode rotations as a sum of irreducible representations.

Data from Problem 9

Consider a planar system of three identical masses and three identical springs. At equilibrium each mass is at the apex of an equilateral triangle. A spring links each pair of masses.

Here is its character table (inversions omitted).

Use coordinate displacements as the basis for a reducible representation. In this representation what are the characters of each of the symmetry operations listed in the table?

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