Consider the vibration of a linear chain in which the force constants between nearest neighbor atoms are alternately C and 10C. Assume the masses are all equal and let the nearest neighbor distance be a/2. Find w(K) at k = 0 and k = Tt/a. Sketch the dispersion relation. (n-1) (n) (n+1) (n+1) 10C M WWM M M WWWM U-1 Vn un Vrt+1 Un+1 (Hint: Because there are 2 springs, displacements of 2 neighboring atoms with be different, say u and v. Us the same method as a diatomic lattice chain as in the lecture notes to first write down the equations of motion for u and v.)