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Unformatted text preview: V C ( t ) = V B + A sin n t + B cos n t where n = 1 LC is the natural angular frequency of this LCoscillator. If at time t=0, the switch is turned on, the voltage must be zero, and since the inductor is an inertial it cannot change its current instantaneously, we must have the current in the inductor is zero as well at this initial instant. Note that since in this circuit: i L = i C = dq C dt = 1 C dV C dt what this means is that not only is the voltage across the capacitor equal to zero at time zero, but also the first derivative of the voltage across the capacitor. This provides us the necessary conditions to obtain the constants A and B. V C ( t ) = V B 1cos n t { } The voltage across the inductor is: V L ( t ) = V B cos n t The current in the capacitor and inductor is given by: i ( t ) = V B C n sin n t...
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 Fall '08
 KRISHNASWAMY

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