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HW2_Assg - guide with negligible friction The unstretched...

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Mechanical Vibrations Homework #2 Due: 17Sep04 - Start of Class Part 1: Work the following problems from the course text. Problem: 2.26, 3.17, 3.35 Part 2: Work the following problems 1. Estimate the viscous damping ratio ( ζ ) and the natural frequency ( ω n ) for transient response of a single degree of freedom system (see Figure 1). Estimate these parameters for multiple peaks and report an average value. 0 1 2 3 4 5 6 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time [s] X [m] Transient Solution Figure 1: Time series plot of the transient vibrations of a system. 1

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2. A mass m , shown by the grey sphere in Figure 2, is constrained to translate along a horizontal
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Unformatted text preview: guide with negligible friction. The unstretched length of each spring is L o and it is assumed that h > L o . Derive the equation of motion for the system in terms of m , k (the stiﬀness of each spring), x , h , and L o . L o h x(t) unstretched spring length h horizontal guide Figure 2: Single degree of freedom mass spring system. 3. Plot the transient response of a system governed by equation (1). Use the following parameters and initial conditions ( ζ = 0 . 05, ω n = 20, x (0) = 3 meters, ˙ x (0) = 1 meters/s). ¨ x ( t ) + 2 ζω n ˙ x ( t ) + ω 2 n x ( t ) = 0 (1) 2...
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