HW2 Spring 2011

5 damped oscillations and resonance the amplitude a

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Unformatted text preview: ulated.) 5. Damped oscillations and resonance. The amplitude A of a driven oscillator as a function of frequency is shown below. A √ A/ 2 Ω 480 520 rad s (a) What is the natural frequency ω0 of the oscillator? (b) What is the Q of the oscillations? (c) What is the energy decay time τE of the oscillations? 6. Relation between free and driven oscillations. A damped harmonic oscillator is displaced from equilibrium, and its position as a function of time is shown below. The damping force is linear, i.e., FD=-bv. The free oscillations can be described by where A&gt;0. x￿cm￿ 4 3 2 1 ￿1 2 4 6 ￿2 8 10 12 14 t￿s￿ ￿3 Physics 2214, Spring 2011 3 Cornell University (a) Determine values for A, τA, ω0 and φ. (b) What is the Q value of this oscillator? (c) Sketch the oscillator's response curve for driven oscillations: plot the amplitude response A(f) vs. drive frequency f. On your graph, give numbers for (i) the resonant frequency, (ii) the full width of the resonance peak at amplitude , (iii) the height of the resonant peak, and (iv) the amplitude at frequencies well...
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This note was uploaded on 11/23/2012 for the course OR 350 at Cornell University (Engineering School).

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