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1. Question 1 [20] A spring-mass system is shown in Figure 1.1. A mass of m = 50 kg is attached to a spring with stiffness of k = 2000 N/m. If the system is placed on an incline with an angle of 8 = 20 and harmonic force ft) = 250 cos 126, [4] 1.1. Derive the equation of motion for the system. 1.2. Determine the maximum amplitude of xy(t). [16] mine m Focos wt ө Figure 1.1 Spring mass system

2. Question 2 [18] A uniform rigid bar with a mass of m = 12 kg is pivoted at point O as shown in Figure 2.1. The bar is connected to two springs with a stiffness k = 4000 N/m and kz = 2500 N/m and also a mass of M = 60 kg is attached at the end of the rod. The system is subjected to a static force f(t) = 500 sin 104t at the end of the rigid bar. Considering a small angular displacement of 0 of the rigid bar about the point o, then, 2.1. Derive the equation of motion, and 2.2. Determine the steady-state response [8] [10] Fosin wt K M m M W K: 0.25 m 0.5 m 1 m Figure 2.1 Spring mass system FULL MARKS [48] Page 3 of 3