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Math Help - Electric Circuit Lapalace Transform Question

  1. #1
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    Question Electric Circuit Lapalace Transform Question

    *Laplace Transform.

    I need help with solving this equation, please.

    In an RLC circuit, L =1H, C = 1/5F, R =2Ohm and f(t) = 2 sin t. Write down the differential equation that describes v(t), the voltage across capacitor, and solve it with initial conditions v(0) = 0 and dv(0)/dt = 3. Ans = - cos t + 2 sin t + e^(-t) (cos 2t + sin 2t)

    So far I've managed to obtain the equation of V(s) = [F(s) + 3LC] / [LC s^2 +RCs + 1 ]
    RC = 2/5
    LC = 1/5
    F(s) = 1 /(s^2 + 1)

    V(s) = [(1/(s^2 + 1)) + 3/5] / [(1/5)s^2 + (2/5)s + 1]

    I tried to solve it by doing partial equation but ended up with wrong answers.
    Last edited by Salcybercat; May 1st 2011 at 04:03 PM.
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  2. #2
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    You've posted what you get when you take the laplace transform, but what is your original differential equation?
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  3. #3
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    My original differential equation is:

    LC v(t)" + RC v(t)' + v(t) = f (t)
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  4. #4
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    What I've managed so far:
    1. Breaking V(s) into parts A and B, part A would then branch to parts C and D


    2. Solving part C


    3. Solving parts D and B from earlier (continued on next image)


    4. Solving the rest of part B and putting all the parts together.


    If my last answer at the bottom of the last image is multiplied by 2, I would be able to obtain the given answer EXCEPT for component (5/4)e^(-t) sin 2t. I'm not sure if I have inversed the transformation with a mistake somewhere, please do check.
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