Question

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(3) An automobile running on 4 wheels is about to pass over a speed bump that has a cross section that fits to a sine function of y(x)-5sinßx with B being a constant, and with a maximum width w 8 cm. as illustrated in Figure 1(a). The velocity of the automobile is 20 km/hr at the time of passing over the bump. The vehicle is supported by a suspension system that is consists of one coilover for each wheel. The analytical model of the suspension system is illustrated in Figure 1(b). The mass of the automobile carried by each of the four wheels is 400 kg. The spring constant of the coil spring in the coilover, k 60,000 N/m, and a damping coefficient c of the damper in the same coilover. The damping effect of the tires is assumed to be negligible. Determine the following: (a) Estimate the required time in "seconds" for either the front wheels or the rear wheels to pass the speed bump. This time is considered to be small enough to justify the assumption that the disturbance to the suspension systems of the vehicle by the speed bump is instantaneous. (b) Determine the value of the minimum damping coefficient (c) of the shock absorber in the coilover for non-oscillatory motion of the vehicle after passing the speed bump (Make sure that you attach the correct unit for the damping coefficient) (c) Derive the expression for the amplitudes of vibration of the vehicle mass after the vehicle runs over the speed bump. (d) Determine the amplitudes of vibration of the vehicle mass in cm at 4 seconds and 4 milliseconds after the vehicle passed the speed bump + vit), amplitude Mass ML Damper with Spring with Spring constant k Speed Bump Damping coefficient c A sine function: Whee (a) Speed bump Figure 1 Vibration of a vehicle passing a speed bump (b) Vehicle suspension system

Answer 1

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