mechanical engineering

Figure 1 illustrates two pendulums with a mass a m1=m2=10kg coupled together by a spring with a stiffness k=20N/m, each with a length of L=0.5m. The spring is situated at a distance a=0.2m along with the pendulum. 1.1. Compute the equation of motion. [6] 1.2. Express the equation in a matrix form. [6] 1.3. Determine two natural frequencies. [6] Page 2 of 3 Solid Mechanics (SME3701) Assessment 5 10 October 2022 2. Question 2 [27] A spring-mass system shown in Figure 2 has a mass of m1=50kg and m2=50kg. The springs supporting the effective spring constant of k1=220N/m,k2=200N/m and k3= 180N/m. Damper with a damping coeffient of c1=50Ns/m,c2=40Ns/m and c3=30Ns/m. 2.1. Construct the model in Wolfram system modeller for 10 seconds using Translational components, giving mass m1 a displacement of 0.1m, plot the displacement graphs for both x1 and x2 on the same graph. [9] 2.2. Determine the matrix for the system. [10]