Two identical beads of mass m each can move without friction along a horizontal wire and are connected to a fixed wall with two identical springs of spring constant k as shown in Fig. 7.5. (a) Find the Lagrangian for this system and derive from it the equations of motion. (b) Find the eigenfrequencies of small amplitude oscillations. (c) For each normal mode, sketch the system when it is at maximum displacement. Note: Your sketch should indicate the relative sizes as well as the directions of the displacements.
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