Question 3 (25 marks) Two plane pendulums of the same length , but of different masses mi = m and m2 = 4m, are coupled by a massless spring with a spring constant k. The pendulums' positions are specified by their angles o and 02. The spring is in equilibrium when the two pendulums are vertical, i.e., 01 = 02 = 0. a, (i) Write down: (a) The total kinetic energy in terms of the generalised coordinates, (b) the gravitational energy, and (c) the spring potential energy. [ Hint: Assume that the angles remain small at all times.] (ii) Write down the full Lagrangian of the system in terms of the physical parameters and coor- dinates