# Electric Circuit Lapalace Transform Question

• May 1st 2011, 03:43 PM
Salcybercat
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.
• May 1st 2011, 07:28 PM
Prove It
You've posted what you get when you take the laplace transform, but what is your original differential equation?
• May 2nd 2011, 12:39 AM
Salcybercat
My original differential equation is:

LC v(t)" + RC v(t)' + v(t) = f (t)
• May 3rd 2011, 02:25 AM
Salcybercat
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
http://i53.tinypic.com/2cd7tyd.jpg

2. Solving part C
http://i54.tinypic.com/28rm903.jpg

3. Solving parts D and B from earlier (continued on next image)
http://i54.tinypic.com/24cxxf6.jpg

4. Solving the rest of part B and putting all the parts together.
http://i55.tinypic.com/287kbw4.jpg

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.