Masses coupled through springs is a model for the behavior ofatoms in a crystal. Consider a one-dimensional crystal, what if wehave a crystal made of two kinds of atoms with different masses?Consider a one-dimensional lattice made up of alternating large andsmall masses, M and m, respectively. Assume periodic boundaryconditions. (a) Calculate the normal modes of this lattice (youshould find two normal modes). (b) Describe the relative motion ofthe two types of masses for each mode.
