Solving RLC Circuit Homework | Help Needed with Finding A and B

[jesuslovesu]

Homework Statement

I'm having some problems solving this RLC circuit, if anyone could help.

R = 2 ohms
C = 2/3 F
L = 1/2 H

The top picture is when t < 0
The bottom picture is when t > 0
Find v_o(t) (notice V_0 is the defined +- voltage over the resistor)
http://img503.imageshack.us/img503/448/rlcwo0.th.png

Homework Equations

The Attempt at a Solution

Well I found that:
i_L(0^+) = 2 A
v_c(0^+) = 0
v_o(0^+) = -4 V
Which I believe are correct,
I found the general equation to be v_0(t) = Ae^{-t} + Be^{-3t}
(My main problem is finding A and B, they should be 2 and -6 but I just can't get that)

A + B = -4
dv(0^+)/dt = -A + -3B
This is where I get a little sketchy, but since Cdv/dt = i_c then I was thinking that since i_L(0^+) = i_C(0^+) for series circuits I could just say
-A + -3B = 2/C
However when I solve those two equations I get A = -4.5, B = 1/2
Does anyone know what I did wrong?

 

[CEL]

Homework Statement

I'm having some problems solving this RLC circuit, if anyone could help.

R = 2 ohms
C = 2/3 F
L = 1/2 H

The top picture is when t < 0
The bottom picture is when t > 0
Find v_o(t) (notice V_0 is the defined +- voltage over the resistor)
http://img503.imageshack.us/img503/448/rlcwo0.th.png

Homework Equations

The Attempt at a Solution

Well I found that:
i_L(0^+) = 2 A
v_c(0^+) = 0
v_o(0^+) = -4 V
Which I believe are correct,
I found the general equation to be v_0(t) = Ae^{-t} + Be^{-3t}
(My main problem is finding A and B, they should be 2 and -6 but I just can't get that)

A + B = -4
dv(0^+)/dt = -A + -3B
This is where I get a little sketchy, but since Cdv/dt = i_c then I was thinking that since i_L(0^+) = i_C(0^+) for series circuits I could just say
-A + -3B = 2/C
However when I solve those two equations I get A = -4.5, B = 1/2
Does anyone know what I did wrong?

You should always solve a series circuit for v_c(t) and a parallel circuit for i_L(t).
Once you have v_c(t) , you can differentiate it in order to get \frac{dv_C}{dt}. Since the current in a series circuit is the same for all elements, you have v_c(0) and \frac{dv_C}{dt}(0).
Knowing v_c(t) you can calculate v_o(t).