Underdamped Parallel RLC Circuit

[Jayalk97]

Hey guys, so I'm having trouble with this circuit analysis question. I need to find voltage across the capacitor as a function of time. I nearly finished analyzing but I'm having trouble solving for the initial value constants in the voltage equation. So first I used KCL to create the equation, then created a characteristic equation to find the type of response, which ended up being under-damped. I'm not trying to get any help with the acgtual numbers, but I end up with the equation v(t) = [A_1 cos(600t)+A_2 sin(600t)]e^(-800t). I'm fairly sure I'm correct so far, but how would I go about solving for A_1 and A_2? Thanks in advance!

 

[berkeman]

Hey guys, so I'm having trouble with this circuit analysis question. I need to find voltage across the capacitor as a function of time. I nearly finished analyzing but I'm having trouble solving for the initial value constants in the voltage equation. So first I used KCL to create the equation, then created a characteristic equation to find the type of response, which ended up being under-damped. I'm not trying to get any help with the acgtual numbers, but I end up with the equation v(t) = [A_1 cos(600t)+A_2 sin(600t)]e^(-800t). I'm fairly sure I'm correct so far, but how would I go about solving for A_1 and A_2? Thanks in advance!
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You should be able to write 2 equations from the initial conditions that will help you solve for those 2 constants.

What is v(0)? What other initial equation can you write for t=0+ ?

 

[Jayalk97]

You should be able to write 2 equations from the initial conditions that will help you solve for those 2 constants.

What is v(0)? What other initial equation can you write for t=0+ ?

V(0) = 0V right? and Current across the inductor is 0.5A. I understand that I am supposed to use those to find the initial conditions, but how are those related to the equation I obtained?

 

[donpacino]

Current across the inductor is 0.5A

current *through the inductor is 0.5A. I know it sounds like a trivial difference, but it is not. current goes through a component. Voltage goes across a component.

I understand that I am supposed to use those to find the initial conditions, but how are those related to the equation I obtained?

Well V(0)=0 is the initial condition. I already know the form of your equation in your first post is not correct, because at t=0+ it does not match expectations. Do you know how to evaluate circuits in the frequency domain, it would make the work easier. If not, why don't you post your KCL/kvl equations.