Unformatted text preview: • It can be tempting to identify the sin( ωt ) part as giving a clue to the phase, but it just arises because the power is F · v and v has one time derivative (changing a cos to a sin ). • A better way to “remember” which term is which is to use cos δ (inphase) and sin δ (outofphase) to tag the two pieces. • After the time differentiation to get ˙ x = v we see that only the outofphase piece can absorb power, onaverage, because only this term has a nonvanishing average over a complete cycle. 2. Quality of a Resonance • We can recast many of the results we’ve derived in terms of: Q = ω /γ ω m = ω p 11 / 2 Q 2 Resonant Frequency A ( ω m ) = a Q 1 p 11 / 4 Q 2 Maximium Amplitude V ( ω ) = a ω Q Maximum Velocity < P ( ω ) > = 1 2 ma 2 ω 3 Q Maximum Power Transfer...
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 Fall '07
 PierreSavaria
 mechanics, Force, Power, Statistical Mechanics, Cos, ΩM

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