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phy293_l06.page1

# phy293_l06.page1 - PHY293 Oscillations Lecture#6 1 Second...

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PHY293 Oscillations Lecture #6 September 22, 2009 1. Second problem set now assigned (http://www.physics.utoronto.ca/ phy293h1f/waves/phy293 ps2.pdf) 2. Lecture outline will be “groomed” this week Third problem set pushed back one week Some additional lectures added textbook reading pushed back Start of material 1. Examples of Resonance in and LRC Circuit Have already seen that an LC resonant circuit is another example of an oscillator The natural frequency is ω 0 = 1 / LC Can now add damping (a resistor) and driving (a signal generator) NB: V is voltage here (not velocity) Use Kirchoff’s laws going around a circuit to find: V 0 cos( ωt ) - q/C - IR - L dI dt = 0 Now make the association ˙ q = I and divide through by L to get ¨ q + R L ˙ q + q/ ( LC ) = V 0 /L cos( ωt ) This is just our forced/damped/SHO equation with γ = R/L ; ω 2 0 = 1 /LC ; a 0 ω 2 0 = V 0 /L ( a 0 = CV 0 ) Look at the circuit analogy of the velocity resonance (NB current is the circuit analog of velocity in the mechanical system) I ( ω ) = I max γ p ( ω
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