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:
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݀
ଶ
ݕ
݀ݐ
ଶ
ܾ
݀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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