p1w06 - Compute the critical damping coefficient c c for...

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CEE 431 Problem Set 1 Winter 2006 (Due: 10:30 AM, Wednesday, Jan. 18, in class) Textbook Reading : Chapters 1 and 2, Sections A.1-A.2 and B.1-B.7 Problem 1. Solve Problem 2.5 in textbook Problem 2. Solve Problem 2.7 in textbook Problem 3. Consider the one-dimensional system shown below. The mass, m = 10 lb- sec 2 /ft and the spring stiffnesses are k 1 = 4500 lb/ft and k 2 = 9000 lb/ft. The motion of the mass will be described by the variable, u(t). c 1 =0 for this problem. a) Compute the natural circular frequency of the system, ω 0 . b) Compute the natural frequency of the system, f 0 . c) Compute the natural period of vibration of the system, T 0 . d) Compute the response of the system if it has an initial displacement of 5 inches to the right and an initial velocity of 35 in./sec to the left. Problem 4. Consider the same system shown in Problem 3, but with c1 0. a)
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Unformatted text preview: Compute the critical damping coefficient, c c , for this system. b) Assume that the damping ratio is 15%. What is c 1 ? c) For this amount of damping, compute the response of the system if it has an initial displacement of 5 inches to the right and an initial velocity of 35 in./sec to the left. Problem 5. a) For the systems described in problems 3 and 4, plot u(t) for t=0 until t= 4 T using a spreadsheet or plotting package. b) For the undamped system, compute the log natural of the ratio of the amplitude of the first and second positive displacement peaks. Compare this ratio with that expected from Equation B.22. c) For the damped system, compute the log natural of the ratio of the amplitude of the first and second positive displacement peaks. Compare this ratio with that expected from Equation B.22. k 2 k 1 u(t) m c 1...
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This note was uploaded on 08/09/2009 for the course CEE 431 taught by Professor Eberhard during the Winter '06 term at Washington University in St. Louis.

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