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Unformatted text preview: equencies is π, that is, completely out of phase with the driving (and at resonance it is π/2 out of phase) (18:50).
(Recall that π corresponds to 180º: a half cycle).
Although we say (roughly) that the maximum amplitude occurs when the driving is “at” the resonance frequency,
the sketch of the A function shows that in fact, it occurs at a slightly lower frequency, referred to as ωmax (note:
above, we carefully used the word near) (20:40). The phase, however, is π/2 at ω0 (exactly), 0 at very low
frequency, and π at high frequency. Recall from your introductory calculus course that to find a minimum or
maximum of a function of one variable, you set the derivative to 0. Taking dA/dω gives
further algebra shows to be
ω0. At ωmax, Amax 1
max 0 (1 2Q )
2 2 max (02 2 ) 1...
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