PHYS-302, Physics of Waves (Summer 2007)
Photographs on this page are ©2007 Dan Russell and were taken when he taught this course in the Summer of 2007
W2 - Phase Diagrams and Impedance
Topical Outline for two-hour class:
- Phase Diarams - plot of velocity versus displacement. Compared usefulness of phase diagram to plot of position and/or velocity versus time. Showed that phase diagram for a damped oscillator looks like a spiral.
- Quality Factor - discussed the quality factor Q for a forced, damped oscillator and found how to measure it from a response curve (power versus frequency) and how it is related to frequency and damping.
- Resonance Defined - We discussed the three conditions for resonance: (i) maximum velocity (current), (ii) maximum power delivered to the oscillator, and (iii) minimum impedance.
- Impedance for an RLC circuit - We derived an expression for the impedance (voltage/current) for a series RLC circuit, and found that the impedance has a real and imaginary part. The real part means that energy is being removed from the system by a damping (resistance) term and the imaginary part means that energy is being stored in the inductor (inertia) and capacitor (spring) parts of the system. Then we looked at mobility, and Nyquist plots.
- Impedance Demonstration -We didn't have a hands-on activity today. Instead Dr. Russell demonstrated the a measurement (using a frequency analyzer) of the impedance of a series RLC circuit. Swapping the leads on the analyzer convered impedance to mobility. We also looked at a parallel RLC circuit and saw that while the resonance frequencies for the two systems are different, the mobility versus frequency graph for the series circuit has exactly the same shape as the impedance versus frequency graph for the parallel circuit.
- Mechanical Impedance - We then derived an expression for the mechanical impedance (force/velocity) of a mass-spring system, and compared the expression to that of the series RLC circuit.
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