PHYS 422 Lecture 17 Forced Vibrations and Resonace III

PHYS 422 Lecture 17 Forced Vibrations and Resonace III -...

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d V i b t i d Forced Vibrations and esonance III Resonance III
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Power Absorption in a Driven Oscillator hat rate must energy be fed into an oscillator to what rate must energy be fed into an oscillator to maintain oscillations at a fixed amplitude recall, the instantaneous power is given by dW dx PF F v dt dt == = consider an undamped oscillator mean power input = 0 F 0 cos ω t k 0 cos FF t F ω = 0 22 0 cos cos m x tC t ωω we get the velocity by differentiating with respect to the displacement
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Power Absorption in a Driven Oscillator k F 0 cos ω t cos xC t ω = 0 sin sin cos v C t P CF t t ωω = − ⇒= F 0 cos ω t energy is fed in during a ¼ cycle and extracted during the next ¼ cycle ⇒⟨ P = 0 t’s add damping to the problem let s add damping to the problem then the velocity is ( ) cos xA t δ =− ( ) sin sin v A t vt = −− = ( ) 0 max of v for a given F 0 and ω
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Power Absorption in a Driven Oscillator 00 F ω F 0 cos ω t 0 1 2 2 () 1 k v ⇒= ⎛⎞ 0 2 0 Q ωω ⎢⎥ + ⎜⎟ ⎝⎠ v 0 has a maximum at ω = ω 0 exactly velocity resonance how much work must be done and power expended to maintain forced oscillations s sin F v t t ( ) [ ] cos cos sin cos cos sin PF Fv t t t δ ωδ
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PHYS 422 Lecture 17 Forced Vibrations and Resonace III -...

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