hw3solution - Homework 3 Solution 1 The equation of motion...

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Homework 3 Solution 1. The equation of motion for the free vibration of the underdamped shock absorber is mx ̈  cx ̇  kx 0 x ̈  2  n x ̇  n 2 x 0, IC: x 0 0and 0 (a) The system parameters stiffness and damping coefficient based on the design specifications. Since the period is T 2s The system’s damping ratio can be found from the logarithmic decrement . Based on the design requirement we have x 1 1and x n 1 0.95 0.05 Because the amplitude reduction is in one cycle, n 1, and the logarithmic decrement is calculated to be 1 n ln x 1 x n 1 1 ln 1 0.05 2.9957 So the damping ratio can then be found as 4 2 2 2.9957 4 2 2.9957 0.43037 The natural frequency of the system is thus computed to be n d 1 2 1 0.43037 2 3.4804 rad/s The stiffness of the system can be established as k m n 2 200 3.4804 2 2423 N/m The damping coefficient can now also be found to be :
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This note was uploaded on 04/30/2008 for the course ME 3504 taught by Professor Tschang during the Spring '08 term at Virginia Tech.

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hw3solution - Homework 3 Solution 1 The equation of motion...

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