# Engineering Circuit analysis, problems with Laplace?

#### Kruum

1. Homework Statement

The switch k is turned at t=0. Calculate $$i_k(t)$$, when t starts from 0. You can find the circuit in my link.

2. Homework Equations

All of them, basically. :tongue:

3. The Attempt at a Solution

http://www.filefactory.com/file/af19a7h/n/index_mht You can find my attempt there. It's in .mhtml format, but any basic browser should open it. I'm not quite sure, if my Laplace to time transformation is correct. The factor before sin is so small. I'd appreciate it, if someone could take a look.

My symbols might differ from your's. But j is imaginary unit (i.e. 1+j), small letters are in time plane, captiol letters are in complex plane an captiol letters with (s) are in Laplace plane.

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#### Tom Mattson

Staff Emeritus
Gold Member

index​.mht
Size: 251.71 KB
Description: No description
...and a login prompt. Do I have to join FileFactory to read this?

#### Kruum

Yep, the second option is free and without registering.

#### Kruum

I just realized, I might have messed up even more than I thought. I'm missing $$e^{-t}$$ from my transformation. I'd greatly appreciate it, if someone can locate my mistake. I've been banging my head to the wall and I really wouldn't like to start from scratch.

#### CEL

For t>0 you are using only the capacitor and the inductor. What about the resistor, that is in parallel with the inductor?
It is the resistor thet will provide the attenuation (the $$e^{-\alpha t}$$ that is missing).

#### Kruum

For t>0 you are using only the capacitor and the inductor. What about the resistor, that is in parallel with the inductor?
It is the resistor thet will provide the attenuation (the $$e^{-\alpha t}$$ that is missing).
Oh yeah, you're right! So $$I_L(s)= \frac {U_{C0}}{L(s^2+ \frac{s}{RC} + \frac {1}{LC}}= \frac {2000 \sqrt{2}}{5}*\frac {1}{s^2+1000s+1000}=\frac {2000 \sqrt{2}}{5*500 \sqrt {3}}* \frac {500 \sqrt {3}}{(s+500)^2+(500 \sqrt {3})^2}$$
Then $$i_k(t)=\frac {4 \sqrt{2}}{5 \sqrt {3}}e^{-500t}sin(500 \sqrt{3}t)$$.

Now it should make sense! Thank you!

Last edited:

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