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# HW6 - ME 375 HOMEWORK#6 Spring 2009 Out Due March 4 2009(at...

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ME 375 HOMEWORK #6 Spring 2009 Out: February 25, 2009 Due: March 4, 2009 (at the beginning of class) PROBLEM 1: (35%) A simple quarter-car model of the suspension system in an automobile is shown below: where m is ¼ the mass of the car body (the sprung mass), k is the suspension spring stiffness, and b is the shock absorber damping. The body displacement y is measured relative to static equilibrium. The displacement r is the input and represents the road surface profile. (a) Determine the equation of motion for this suspension system. (b) Assuming that m = 400 kg and k = 160,000 N/m, write the differential equation from part (a) in terms of these numbers and the as-yet-unknown damping coefficient b . (c) Generate expressions that relate natural frequency and damping ratio to the numbers given in part (b) as well as the damping coefficient b . (d) As part of a design project, you’ve been asked to select an appropriate shock absorber for this car that provides a damping ratio close to 0.707. Your choices of shock absorber have the following

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