Unformatted text preview: differential equation: LC * d 2 V c + RC * dV c + V c = V T Dt 2 dt If , V T = a sin (wt) , where a = V MAX (the amplitude of the forcing function) Then, our equation now becomes: LC * d 2 V c + RC * dV c + V c = V MAX * sin (wt) Dt 2 dt In determining the short term behavior (can be consider the homogenous portion) of our equation, we find the following: LC * d 2 V c + RC*dV c + V c = Dt 2 dt d 2 V c + R *dV c + 1 *V c = Dt 2 L dt L C Let, P = R/L , Q = 1/LC and V c (t) = e st Then, d 2 e st + P*d(e st ) + Q (e st ) = dt 2 dt Which leads to eigenvalues, S 2 e st + P S e st...
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 Spring '10
 Nawaz
 Volt, RLC, RC circuit, RL circuit, LC circuit

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