Unformatted text preview: below the peak frequency. Assume that
the drive amplitude is F0/k = 10 cm.
(d) What is the gain at resonance, defined as the amplitude at resonance divided by the
amplitude at frequencies well below resonance?
(e) In general, how do the amplitude at resonance and the width of the resonance for
damped oscillations depend upon: (i) the amplitude decay time τA; and (ii) the resonant
frequency? (Qualitative answers will be sufficient here).
7. Driven oscillations. In lecture we derived the following expression for the complex
amplitude of the response of a driven damped oscillator: A( ω D ) = F0 /m
ωD
2
2
ω0 − ωD + i 2τA (a) D etermine expressions for the A(ωD ) magnitude and phase of A( ω D ) (b) Show (by taking the derivative and setting it to zero) that the maximum magnitude A(ωD )
of occurs at a frequency where . (c) What must Q be so that so that this maximum frequency deviates from ω0 by (i) 0.5% and
(ii) 5%?
(d) Determine the maximum magnitude Am of (expressing it in terms of (the magnitude at low frequen...
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This note was uploaded on 11/23/2012 for the course OR 350 at Cornell.
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