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June 30th, 2007, 10:41 AM   #1
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RLC circuit and differential system of equations

( LRC circuit ) Consider the circuit equation

.. .
LI + RI + I / C = 0, where L, C > 0 and R ≥ 0.

(a)Rewrite the equation as a two-dimensional linear system.

(b)Show that the origin is asymptotically stable if R > 0 and neutrally stable if R = 0.

(c)Classify the fixed point at the origin, depending on whether R^2 C – 4 L is positive, negative, or zero, and sketch the phase portrait in all three cases.
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