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A small trailer and its load have a total mass of 250 kg. The trailer is supported by two springs, and when the boat is given an initial displacement x0 downward and released from rest, the amplitude of oscillation is reduced to ¼ x0 after one half cycle and the period of the oscillation is 0.8 s. The trailer is then pulled over a road, the surface of which can be approximated by a sine curve with an amplitude of 35 mm and a wavelength of 5 m (i.e., the distance between successive crests is 5 m and the vertical distance from crest to trough is 70 mm). Determine (a) the damping ratio, (b) the spring stiffness, (c) the amplitude of the vibration of the trailer at a speed of 50 km/h. (Hint: Use the logarithmic decrement discussed in Probs. 19.129 and 19.130.)
Fig. P19.162
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Vector Mechanics for Engineers: Statics and Dynamics
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