Consider the linear model of a molecule with three atoms. The outer atoms are of mass m and the atom in the molecules center is of mass M . The outer atoms are connected to the center atom through springs of a constant k. (a) Find the Lagrange function of the system. Use as coordinates the deviations of the atoms from their equilibrium position. (b) Find the eigenfrequencies of the system and corresponding eigenvectors. (c) Write down the general solution of the equation of motion of the system. I have not attempted this problem because I dont know how to do it at all. Any help will be appreciated. Thank you.