Problem 2 Three point masses are connected by springs of spring-constant k, and they can move only in the i x direction. The masses on the ends have mass m and the one in the middle has a different mass M. a) Write down the Lagrangian for this system and obtain the equations of motion from it. b) Find the normal modes and frequencies (eigenvalues and eigenvectors). c) If one of the eigenfrequencies is zero, what is your interpretation of that observation