HW6soln

# HW6soln - ME 375 Homework 6 Solution Problem 1 Part A...

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ME 375 Homework 6 : Solution March 12, 2009 Problem 1 Part A Determine the equation of motion for the suspension system Solution: m ¨ y + b ˙ y + ky = b ˙ r + kr Part B Assuming that m=400kg and k=160,000 N/m, write the diFerential equa- tions from part (a) in terms of these numbers and the as-yet-unknown damp- ing coe±cient b. Solution: 400¨ y + b ˙ y + 160000 y = b ˙ r + 160000 r Part C Generate expressions that relate natural frequency and damping ratio to the numbers given in part (b) as well as the damping coe±cient b. Solution: We know that for a second order equation, the following equation holds true with respect to some input f: ¨ y + 2 ζω n ˙ y + ω 2 n y = f compared to our equation: ¨ y + b 400 ˙ y + 400 y = b 400 ˙ r + 400 r 1

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the natural frequency is: ω n = 20 and the damping ration is ζ = b 16000 Part D As part of a design project, you’ve been asked to select an appropriate shock absorber fo this car that provides a damping ratio close to 0.707. Your choices of shock absorber have the following damping coeFcients: 10,000 N/(m/s), 11,000 N/(m/s), 12,000 N(m/s). Which one would you choose, and why? Solution:
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## This note was uploaded on 08/28/2010 for the course ME 375 taught by Professor Meckle during the Spring '10 term at Purdue.

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HW6soln - ME 375 Homework 6 Solution Problem 1 Part A...

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