p3w06 - Problem 2. Consider a system without damping. a)...

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CEE 431 Problem Set 3 Winter 2006 (Due: 10:30 AM, Wednesday, Feb. 1, in class) 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 an alternating load of +/- P o = 1000 lbs, which changes direction every 0.1 seconds, as shown below. Problem 1. a) Compute first three non-zero Fourier series coefficients for the alternating load. b) On one plot (spreadsheet or plotting package), show the alternating load, and the Fourier approximations using one non-zero tem, two terms and three terms.
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Unformatted text preview: Problem 2. Consider a system without damping. a) Compute the steady-state response of the SDOF system to each of the three Fourier load components calculated in Problem 1. b) In a table, report: - the magnitude of the Fourier series coefficient for each load component (from Problem 1), - the displacement amplification for each component, and - the resulting maximum displacement amplitude for each component. c) On one plot (spreadsheet or plotting package), show the SDOF displacement response using one term, two terms and three terms. Problem 3. Repeat Problem 2 for a damping ratio of 15%. k 2 k 1 u(t) m c 1 Q(t) +P t-P 0.1s 0.2s 0.4s 0.3s...
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