(1) Consider the system of Fig. 9.1 consisting of two massless pendulums coupled by a spring. i. ii. Derive the equations of motion for small oscillations. Express these equations in matrix form. Given k = 500 N/m, l = 0.5 m, and m = m = 10 kg. a is 0.1 m along the pendulum. Determine the natural frequencies, mode shapes, and sketch the mode shapes. m2 Figure 9.1: Two pendulum system for Problem 1.