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Below is the phonon-dispersion relation for a 1D diatomic harmonic crystal: M1 + M2 2M M2 W 7 = C M, M2 (M1 + M, )2 (1 - cos ka) a. Simplify the 1D phonon-dispersion relation such that it is in terms of the mass ratio u = M2/M1- b. plot the 1-D phonon-dispersion relation for: u = 0.25, M = 0.5, u = 1, u = 2, u = 4, from ka = -It to ka = 1. The unit of the x-axis is ka, and the unit of the y-axis is VC/M1- c. Explain what happens to the dispersion relation as u changes