Two beads of mass 2m and m can move without friction along a horizontal wire. They are connected to a fixed wall with two springs of spring constants 2k and k as shown in Fig. 7.6: (a) Find the Lagrangian for this system and derive from it the equations of motion for the beads. (b) Find the eigenfrequencies of small amplitude oscillations. (c) For each normal mode, sketch the system when it is at the maximum displacement.