Equivalent Resistance of an RLC circuit

[wiz0r]

Homework Statement

It is in the attachment.

NOTE: I supposed I did a little mistake when I drew the circuit with PSpice. The closed switch should look like .---->. instead of having that 45 angle. I don't know if it matters or not, so yea..

Homework Equations

Rp = (R1 * R2)/ (R1 + R2)
Rs = R1 + R2 + R3 + ... + Rn
α(series) = Req / (2*L)
Wo = 1/sqrt(LC)

The Attempt at a Solution

Okay, well, I'm trying to solve this second order transient circuit, but I have a problem! I can't find the correct equivalent resistance. What I do first is to remove the voltage source by a short and the current source by an open circuit. Now, I got to find the equivalent resistance to calculate α. What I do is;

R12 = (2 * 6) / (2 + 6) = 1.5 ohms

then;

Req = R12 + R3 + R4 = 1.5 + 4 + 2 = 7.5 ohms

According to the book, the Req should be 2 ohms! So either, I'm doing something really wrong, or there's a mistake with the book. Can someone please help me?

Any help would be greatly appreciated.

 

[wiz0r]

mm, well, i figured out what was wrong.

since the switch is closed, i need it to open it to find the equivalents R, L, and C to check if its an series RLC or parallel RLC.

i opened the switch, and took out the sources, everything cancels out, and i'll have only the rightmost loop with the 2 ohm resistance, 2H inductance, and 1F capacitance.

anyway, could someone tell me if I am right or not?