Spring 2012 ME 448: Mechanical Vibrations Harmonic Analysis 1. For the periodic force function shown determine coefficient a0 and coefficients an and bn for n = 1 2 3 4 5. Use the equation ??? ? ? ? 1 0 sin( ) 2 ( ) n n n f n t f F t ? ? to express the forcing function and plot the result. 2. Determine the steady-state response for the system below using the forcing function developed in question 1. The system consists of a 26 lb weight and a spring with stiffness 6.5 lb/in. Neglect all damping. Plot the system response for 3 seconds of motion. 3. The variation of pressure with time in a hydraulic line is shown below. The data were taken directly from recorded pressure at 0.01 second interval. Using harmonic analysis determine a Fourier expansion which will express the data. Numerically determine coefficient a0 and coefficients an and bn for n = 1 2 3. Plot the result. Time (s) Pressure (psi) Time (s) Pressure (psi) Time (s) Pressure (psi) Time (s) Pressure (psi) 0.01 2.9 0.07 28.7 0.13 54.3 0.19 28.6 0.02 10.4 0.08 31.5 0.14 46.8 0.20 25.7 0.03 19.2 0.09 38.0 0.15 38.0 0.21 19.2 0.04 25.7 0.10 46.8 0.16 31.5 0.22 10.4 0.05 28.6 0.11 54.3 0.17 28.7 0.23 2.9 0.06 28.6 0.12 57.2 0.18 28.6 0.24 0.0
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