PHYS 422 Lecture 17 Forced Vibrations and Resonace III

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

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F d Vib ti d Forced Vibrations and Resonance III
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Power Absorption in a Driven Oscillator what 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 P F Fv dt dt = = = consider an undamped oscillator mean power input = 0 F 0 cos ω t k 0 0 cos F F t F ω = 2 2 0 cos cos m x t C t ω ω ω ω = = 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 x C t ω = i C 0 sin sin cos v t P CF t t ω ω ω ω ω = − = − F 0 cos ω t energy is fed in during a ¼ cycle and extracted during the next ¼ cycle ⇒ ⟨ P = 0 let’s add damping to the problem let s add damping to the problem then the velocity is ( ) cos x A t ω δ = ( ) i A δ ( ) 0 sin sin v t v t ω ω ω δ = − = − max of v for a given F 0 and ω
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