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Unformatted text preview: m = 10kg, k = 250 N/m, and c = 60 kg/s is subject to a driving force given by F cosωt , where F = 48 N. a) What value of ω results in steadystate oscillations with maximum amplitude? For the conditions determined in part a), b) What is the maximum amplitude? c) What is the phase shift? 4) (15 points) Taylor 5.44 Another interpretation of the Q of a resonance comes from the following: Consider the motion of a driven damped oscillator after any transients have died out, and suppose that it is being driven close to resonance, so you can set ω f = ω , a) Show that the oscillator’s total energy (kinetic plus potential) is E = 1 2 mω 2 f A 2 . b) Show that the energy Δ E dis dissipated during one cycle by the damping force F dmp is 2 πmβω f A 2 . (Remember that the rate at which a force does work is Fν .) c) Hence show that Q is 2 π times the ratio E/ Δ E dis . 55 Points Total...
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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 mechanics, Work

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