hw6 - ME365 Homework Set 6 Out: September 29, 2011 Due:...

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ME365 Homework Set 6 Out: September 29, 2011 Due: October 14, 2011 Problem No. 1 Given: A shock absorber is described by the following differential equation: ݉ ݀ ݕ ݀ݐ ൅ܾ ݀ݕ ݀ݐ ൅݇ݕൌܭݔ where m is the mass of the shock absorber, b is the damping coefficient of the dashpot, k is the spring constant, K is the static gain, x is the displacement input (the depth of a pothole or the height of a speed bump or curb) and y is the displacement output of the shock absorber (the displacement the occupant of the vehicle feels). For a particular shock absorber, m = 1250kg, k = 5000 N/m and K = 1 N/m. Find: (a) Determine the natural frequency, ߱ , and damping ratio, ߞ, of this system symbolically. Find the value of the damping constant, b, needed to attain a damping ratio of 0.7. (b) Using your value from (a), find the total time response of the shock absorber (particular solution +homogeneous solution) for a pothole of depth 10 cm. Assume that the shock absorbed starts from rest and that the pothole is a
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hw6 - ME365 Homework Set 6 Out: September 29, 2011 Due:...

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