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Question- Determine the equations of motion for transverse oscillations of a planar square lattice of identical atoms of mass M with a force constant C using nearest neighbor interaction. Assuming a solution for the displacement u(lm) of the form (l,m represents the position of the atom) u(lm) = u(lm)(0) Exp{ilkxa + imkya - wt} Derive the relationship between w and kx, ky that satisfies the equation of motion.

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