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Homework Help: Differentials/ second order/ electrical vibration

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data
    A simple series circuit has an inductor of 1 henry, a capacitor of 10^-6 farads, and a resistor of 1000 ohms. The initial charge on the capacitor is zero. If a 12V battery is connected is connected to the circuit, and the circuit is closed at t=0, find the charge on the capacitor 1 second later and the steady state charge.

    From this I know initial current =0


    3. The attempt at a solution
    Q''+1000Q'+10^6Q=0
    Q(t)=C1(e^(-500t))cos(500sqrt(3)t)+C2(e^(-500t))sin(500sqrt(3)t)
    I got that far. now if I used Q(0)=0 and Q'(0)=0 I get C1=C2=0 which I think is wrong. Can someone help? Thank you in advance.
     
  2. jcsd
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