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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>0. xcm
4
3
2
1
1 2 4 6 2 8 10 12 14 ts 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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