PHYS 422 Lecture 16 Forced Vibrations and Resonace II

PHYS 422 Lecture 16 Forced Vibrations and Resonace II -...

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d V i b t i d Forced Vibrations and esonance II Resonance II
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Harmonic Forcing with Damping F 0 cos ω t ( ) 22 0 0 cos F A m ω ωδ = 0 sin F A m γ = + 0 () F m A ⇒= ( ) ( ) 1 2 2 2 0 ωω ⎡⎤ −+ tan γω δ 0
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Harmonic Forcing with Damping F 0 cos ω t ( ) 1 2 2 0 m γ ωω =− ( ) A ω ( ) ( ) 0 1 2 2 2 22 () F m A γω = + 2 0 ⎢⎥ ⎣⎦ 0 2 tan δ= ( ) δω 0 0
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Effects of the Resistive Term F 0 cos ω t call the quality factor recall the quality factor Q ω 0 / γ larger Q, less dissipation in terms of Q 0 F ( ) 1 2 2 2 22 0 0 () m A ω ωω = ⎛⎞ −+ ⎜⎟ ⎢⎥ Q ⎝⎠ ⎣⎦ 0 n Q ( ) 0 tan δω better to use ω / ω 0 as a variable 0 0 1 2 2 2 0 0 F A m = 0 1 tan Q = N 0 0 2 0 1 F k Q + 0
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Effects of the Resistive Term F 0 cos ω t
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Transient Phenomena so far, we have neglected the effects of the onset of the driving force the driving force was initiated in the distant ast and all transient effects have died away past and all transient effects have died away
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