Single Degree of Freedom: 1. A slender but rigid prismatic bar AB of weight W and length l is hinged at A and supported in a horizontal position by a vertical spring attached to it at C. For small amplitudes of rotational oscillations of the bar in a vertical plane, calculate the period of oscillation if the spring has constant stiffness K and negligible mass. (Vibration Problems in Engineering – Young, Timoshenko- Fifth Edition – Sum no 1.3.4) 2. Determine the undamped response of a one-degree system to the forcing function in the figure. (Vibration Problems in Engineering – Young, Timoshenko- Fifth Edition – Sum no 1.12.3) 3. The system showed simulates a vehicle travelling on a rough road. Let the vehicle velocity be uniform. Calculate the response z(t) as well as force transmitted to the vehicle. (Fundamentals of Vibration – Meirowitch – international edition 2001) 9. Determine the undamped response of a one-degree system to the parabolic forcing function Q = Q1(t-t1)2/ t12 in the figure. and viscous damping is such that after 10 cycles of free vibration.22) . due to unbalance in the rotor. Timoshenko. the amplitude is reduced to half of its initial value. Find the natural frequency of vibration of the weight in the vertical direction.Fifth Edition – Sum no 1. The stiffness of the beam is such that static deflection at the midspan is 0. Timoshenko.6) 5. (Vibration Problems in Engineering – Young. Neglecting the distributed mass of the beam.4. A scissors jack is used to lift a load W. A simply supported beam carries an electric motor of weight W=2000 lb at midspan.Fifth Edition – Sum no 1. S.1) 6. Rao – Fifth Edition – Sum no 2. The motor runs at 600rpm and. (Vibration Problems in Engineering – Young. find the amplitude of steady state forced vibrations.12. (Mechanical Vibrations .S. sets up a centrifugal force Q=500lb at this speed.10 in. The links of the jack are rigid and the collars can slide freely on the shaft against the springs of stiffnesses k1 and k2. Rao – Fifth Edition – Sum no 3. Assuming that the body of the spacecraft is very large (rigid). S. determine the natural frequency of vibration of each panel about the axis of the connecting aluminium rod. S. Assume that the bicycle is free of vertical vibration before encountering the step change in the vertical displacement. a = 0.S.5 m. Derive the equation of motion and find the steady-state response of the system shown for rotational motion about the hinge O for the following data k1 = k2 = 5000 N/m.000 N/m. and damping constant of 800 N. respectively.106) 9. m = 10 kg. (Mechanical Vibrations . ω = 1000 rpm. determine the displacement of the boy in the vertical direction. The differential setting of the concrete blocks on the road caused the level surface to decrease suddenly. and 1.000 N-s/m. Figure shows a spacecraft with four solar panels. as indicated in Figure.68) 8. F0 = 500 N (Mechanical Vibrations . Each panel has the dimensions 5 ft * 3 ft * 1 ft with a weight density 0.in. b = 0. l = 1 m. (Mechanical Vibrations . Rao – Fifth Edition – Sum no 2.S. 50. M = 50 kg. A boy riding a bicycle can be modelled as a spring-mass-damper system with an equivalent weight.25 m. If the speed of the bicycle is 5 m/s (18 km/hr).7. Rao – Fifth Edition – Sum no 2. S. and is connected to the body of the spacecraft by aluminium rods of length 12 in.24) .S.1 lb/cu. stiffness. and diameter 1 in. 3984t N.S. is mounted on the top of a bank building for surveillance.50. f(t).005 m. (Mechanical Vibrations . is found to be harmonic with f(t) = 25 cos 75. 3.10. A video camera. of mass 2. The wind-induced force acting on the video camera. Rao – Fifth Edition – Sum no 3. The video camera is fixed at one end of a tubular aluminum rod whose other end is fixed to the building as shown in Fig.0 kg. Determine the cross-sectional dimensions of the aluminum tube if the maximum amplitude of vibration of the video camera is to be limited to 0. S.37) .