Second Order RLC source switching cct

[jess_88]

Hey guys

I'm just wondering if I'm on the right track for the problem. I have started analysing the circuit, but I'm really unsure of my method of analysis. Did I use the formulas correctly?

The circuit switches from position "a" to position "b" at t=0
and I'm trying to fined i(t) for t>0
[PLAIN]http://forum.allaboutcircuits.com/cache.php?url=http://i.imgur.com/Dpyep.png

from what I understand, I need to determine i(o), which is for the circuit at t=0 (containing an inductor and 4A supply).

Then determine the α and wo for the circuit at t>0
where α = 1/2RC and wo = √(1/LC).
which will indicate the formula to use for the step response, to allow for determining i(t).


my calculated values so far-
by KCL
i(0) = 4A(6/2+8)
= 3A

This is where I think I may have gone wrong-
at t>0
I used source transformation for the 4A supply (24V)
then added the total voltage in the loop (= +12V)
[PLAIN]http://forum.allaboutcircuits.com/cache.php?url=http://i.imgur.com/WjGl5.png

α = 1/(2 x 20Ω x 0.02F)
= 1.25

wo = √(1/ (2 x 0.02))
=5

therefor I understand I need to use
v(t) = (A1cos(wd)t + A2sin(wd)t)e^(-αt)

wd = √((wo^2) - (α^2))

= √(375/16)

... which isn't a very nice looking number

have I made a mistake somewhere? Is my whole understanding of the method in answering this question just plane wrong?

 

[Valkarie]

Thanks in advance for any advice/help. :)Hi there,It looks like you have set up the problem correctly and you have determined the appropriate equations to use. Your calculations also look correct. The only thing I might suggest is that when you are calculating wd (angular frequency), you can simplify it to √(25/8) instead of having a decimal in the answer. Otherwise, it looks like you are on the right track!