(30 points) Three identical pendulums (same mass m and length () are E E suspended on a wood stick. The deformation of wood introduces a small potential energy only between nearest neighbors, i.e., U12 = 66162 and U23 = 66263, where e is the coupling constant, 6; (i = 1, 2, 3) is the displacement of pendulum #i from its equilibrium position. Use the D3 small-angle approximation for this problem. (a) (10 points) Write down the Lagrangian of the system. Derive the equation of motion in the matrix form. (b) (10 points) Find the three normal frequencies of the system. You may use wo = g/l and o = 6/m to simply your calculation. (c) (10 points) Describe the relative amplitude and phase of the pendulums of the three normal modes