PHY293 Oscillations Lecture #6September 22, 20091. Second problem set now assigned (http://www.physics.utoronto.ca/ phy293h1f/waves/phy293ps2.pdf)2. Lecture outline will be “groomed” this week•Third problem set pushed back one week•Some additional lectures added⇒textbook reading pushed backStart of material1. Examples of Resonance in and LRC Circuit•Have already seen that an LC resonant circuit is another example of an oscillator•The natural frequency isω0= 1/√LC•Can now add damping (a resistor) and driving (a signal generator)◦NB:Vis voltage here (not velocity)•Use Kirchoff’s laws going around a circuit to find:V0cos(ωt)-q/C-IR-LdIdt= 0•Now make the association˙q=Iand divide through byLto get¨q+RL˙q+q/(LC) =V0/Lcos(ωt)•This is just our forced/damped/SHO equation withγ=R/L;ω20= 1/LC;a0ω20=V0/L(a0=CV0)•Look at the circuit analogy of the velocity resonance (NB current is the circuit analog of velocity in the mechanical system)I(ω) =Imaxγp(ω
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