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# hw_4 - T and m eff Now suppose the man begins to oscillate...

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ME163 Mechanical Vibrations (Winter 2009) Due Wednesday 2.4.09 7pm (in the box or to a TA) Worth 75 Extra Credit points Answers emailed by 9pm, midterm the day after 1. Consider the system in figure below, with m eff = 20 [kg], damping coefficient c = 500 [Ns/m] and spring stiffness k = 2000 [N/m]. Suppose the system is forced by a sinusoidal force f ( t ) = 350 cos ωt . You may neglect gravity. (a) Derive the equation of motion for the length of the spring (ie the distance between the mass and the connection point for the spring/damper). (b) Calculate the steady state response of the spring length at ω = 10 [rad/s] using phasors. k m c f ME163 Mechanical Vibrations 1 HW4

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2. A man of mass m m = 80 [kg] is walking on a tightrope of length = 5 [m] and mass m r = 10 [kg]. Trying to impress the crowd, the tightrope walker decides to stop at the middle of the rope, where the measured displacement in the y direction is Δ = 80 [cm]. Assume the rope is bending as a sinewave instead of a triangle). (a) Use the Rayleigh method to compute kinetic energy
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Unformatted text preview: T and m eff . Now suppose the man begins to oscillate shake his legs imposing a force f ( t ) = 230cos ωt . Considering that all damping is structural, with structural damping factor γ = 0 . 45, and k eff = 1800 [N/m]: (b) Find equation of motion. (c) What is the magnitude of the oscillation for ω = 18 . 84 [rad/s]? l 2 l 2 ME163 Mechanical Vibrations 2 HW4 3. Figure 2 presents data from a forced vibration experiment. The y-axis includes both the spring force and viscous force v/s displacement. Determine the e±ective damping and e±ective sti±ness for the system. In the experiment, the system was excited at a frequency ω = 8[ rad s ]. The ²gure will be online and you may open it in Matlab and use the cursor to get necessary information (or just by inspecting the plot below).-0.04-0.03-0.02-0.01 0.01 0.02 0.03 0.04-1.5-1-0.5 0.5 1 1.5 x(t) Total Force (damper and spring) ME163 Mechanical Vibrations 3 HW4...
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hw_4 - T and m eff Now suppose the man begins to oscillate...

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