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Amcote
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Homework Statement
Locate the poles of the response function [itex]\alpha(\omega)[/itex] in the complex plane for an LRC circuit.
Homework Equations
[tex]\alpha(\omega)=\frac{-i\omega}{L}\frac{1}{\omega_0^2-\omega^2-i\omega\gamma} [/tex]
[tex]\omega_0^2=\frac{1}{CL} [/tex]
[tex]\gamma=\frac{R}{L}[/tex]
The Attempt at a Solution
So we've been going over how to locate poles and residues with normal functions and this is the first time doing something that is applicable to physics. Normally I'm used to having a function of x and changing this into a function of z and finding the poles that way. I'm not really sure how to start this question whether I should be changing ω to z or whether this is already a complex function. I've tried using the quadratic formula on the denominator in which I get
[tex]\frac{-\gamma \pm \sqrt{\gamma^2-4\omega_0^2}}{-2i} [/tex]
but I do not think this is correct.
Any help would be nice.
Thanks