Consider a 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) Determine the Lagrange function of the system. Use as coordinates the deviations of the atoms from their equilibrium position.
(b) Determine the Eigen frequencies of the system and corresponding eigenvectors.
(c) Write down the general solution of the equation of motion of the system.