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Question 1 A coupled pendulum system consists of two light pendulum rods, of length 11 and 12, respectively, connected by a spring with a stiffness k, as shown in Figure Q1. Two masses, mi and m2, are attached to the end of each rod. a (a) Using first principles, evaluate the natural frequencies of the system using the constants provided in Table Q1. [14] (b) Hence, determine and plot the normal mode shapes for the system. [6] Note: The mass of the rods can be assumed to be negligible and the mass moment of inertia of a simple pendulum of mass m and length lis ml. Assume small angles of deformation. a k !1 mi 02 m2 Figure Q1: Coupled pendulum system setup. mi 10 kg a Table Q1: Parameters for Question 1. 7 22 0.2 m 0.6 m m2 5 kg 0.07 m k 5 kN/m