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shniflbaag
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Homework Statement
This was an electrical engineering lab, dealing with the steady state response of an RLC circuit (diagram attached). The main part of the lab consisted of experimentally determining the circuit's critical resistance value, and viewing the overdamped and underdamped responses. Now, I've hit the point where I'm determining the theoretical values for what we measured. I'm starting with the underdamped case, and found s1 and s2 using equation 1 (below). My final objective here is to determine i(t), which, I gather, requires that you solve for the constants A1 and A2, which appear in several of the equations below. Also, FYI I have already solved for ωo, ωd and [itex]\alpha[/itex].
Thanks in advance.
Homework Equations
(1) s=-[itex]\frac{R}{2L}[/itex][itex]\pm\sqrt{(\frac{R}{2L})^{2}-\frac{1}{LC}}[/itex]
(2) i(t)=A1e(s1t)+A2e(s2t)
The Attempt at a Solution
After looking around for a while, it seems as though the way to solve for these two is by creating a system of equations comprised of v(0) and the derivative of i(0), however every single source I've found has described it differently and my own lab simply says "solve for it" and nothing else on the subject.
so far I'm fairly sure that one of the equations is V(0)=A11+A2=1 (we used a 1V signal). The other equation varies, and I've had trouble finding one that makes sense. The closest I think I've gotten was:
[itex]\frac{i_{c}(0)}{C}[/itex] = S1A1+S2A2
However nowhere is that equation mentioned in my lab and I don't see how it would make sense.
Thanks again