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phy293_l07.page4

# phy293_l07.page4 - (b There are three frequency regimes for...

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(b) There are three frequency regimes for forced oscillations low ω Resonant ω High ω δ 0 δ = π/ 2 δ π A a 0 A = a 0 Q 1 1 - 1 / 4 Q 2 A = a 0 ω 2 0 ω 2 Stiffness dominated spring/damping balanced Inertia dominated (c) Velocity Response Resonance at ω = ω 0 ˙ X ( t ) = - ωA ( ω ) sin( ωt - δ ) ≡ - V ( ω ) sin( ωt - δ ) V ( ω ) = a 0 ω 2 0 p ( ω 2 0 - ω 2 ) 2 2 + γ 2 For low ω , V 0 ; for high ω V a 0 ω 2 0 At resonance the reactive elements of the system cancel each other out The system becomes easy to drive : viscosity/damping and restoring force/spring work together resulting in resonance (d) Power Absorbed by an oscillator Power averaged over a complete cycle is only absorbed by out-of-phase component of solution < P ( ω ) > = P max γ 2 ( ω 2 0 - ω
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