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2 (a) The viscously damped system in Figure Q2(a) has a mass of 4 kg, stiffness k = ky = kg = 1000 N/m and a damping ratio of 0.25. If the mass is stretched 40 mm to the right of the static equilibrium position and released from rest, determine: (1) The natural frequency in Hz. (ii) The equation that describes the damped oscillatory motion. (iii) The position of the mass in mm at t = 0.1s. (b) Figure Q2(b) shows a shock absorber for a motorcycle of mass m=150 kg. When the shock absorber is subjected to an initial vertical velocity due to a road bump, the resulting displacement amplitude vs time graph is shown in Figure Q2(c). The successive amplitudes are related as follows: (2) (6) (2) X1.5 = X1/3; X2 = X1.5/3; X2.5 = X2/3 For the underdamped shock absorber, determine: (i) The damping ratio. (ii) The spring stiffness if the damped period is 25. (5) (5) + X Static equilibrium position k3 ki m Figure Q2(a) k/2 com- x(1) k/2 B home us Figure Q2(b) Figure Q2(c)