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# p2w06 - than the velocity for Problem Set 1 Problem 2...

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CEE 431 Problem Set 2 Winter 2006 (Due: 10:30 AM, Wednesday, Jan. 25, in class) Textbook Reading : Sections A.1-A.2 and B.1-B.7 Problem 1. 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). The mass is subjected to a sinusoidally varying force with P o = 1000 lbs and ω =20/sec. For this problem, c 1 =0. a) Compute the tuning ratio, β = ω / ω 0 . and the damping ratio, ζ . b) Compute the particular solution, u p (t) for this loading. This solution satisfies the equation of motion, but it does not necessarily satisfy the initial conditions (displacement, u o and velocity). c) Compute the total response of the system if it has an initial displacement of 5 inches to the right and an initial velocity of 120 in./sec to the left. Note that this velocity is larger
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Unformatted text preview: than the velocity for Problem Set 1. Problem 2. Repeat Problem 1, but with c 1 =100 lb-sec/ft. Problem 3. Consider the systems described in problems 1 and 2. Using a spreadsheet or plotting package, plot on a single graph (from t=0 until t= 4 T ). a) u p (t) for no damping b) u(t) for no damping c) u p (t) with damping d) u(t) with damping Problem 4. Discussion. a) Which of the solutions listed and plotted in Problem 3 satisfy the initial conditions? b) From t=0 until t= 4 T , what is the ratio of the maximum displacement of the undamped system to that of the damped system? c) Between t=100T o and t=110 T o , what is the ratio of the maximum displacement of the undamped system to that of the damped system? k 2 k 1 u(t) = P o sin( ω t) m c 1...
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