I have a homework assignment that I am having trouble with for my circuit analysis class. It seems a lot of my troubles are stemming from not remembering how to solve some diff EQ's. Here is a link to my homework post where you can find ALL the information. I have just listed the equations I came up with here to cut down on the garbage.

http://forum.allaboutcircuits.com/showthread.php?t=41608

Based on my (hopefully correct) work beforehand, I am left with three general solutions and I don't know how to solve for the coefficients.

Gen. Sol. 1:

R = 10 Ω; L = 100 mH; and C ≈ 253.3 nF;
ω = 2000∏
.: ζ ≈ 0.007921 < 1 and the circuit is underdamped.

I know that the general form for the solution for an underdamped circuit is:

x(t) = e^(-ζωt)*[A1 cos(ω*√[1-ζ^2]*t) + A2 sin(ω*√t[1-ζ^2]*t)]

I need to find A1 and A2.

Gen. Sol. 2:

R = 10 Ω; L = 795.77 uH; and C ≈ 31.831 uF;
ω = 2000∏
.: ζ = 1 = 1 and the circuit is critically damped.

I know that the general form for the solution for a critically damped circuit is:

x(t) = B1*e^(-ζωt) + B2*t*e^(-ζωt)

I need to find B1 and B2

Gen. Sol. 3:

R = 10 Ω; L = 79.577 uH; and C ≈ 318.31 uF;
ω = 2000∏
.: ζ = 10 > 1 and the circuit is overdamped.

I know that the general form for the solution for a overdamped circuit is:

x(t) = K1*e^(-(ζω-ω√[ζ^2-1])t) + K2*e^(-(ζω+ω√[ζ^2-1])t)

I need to find K1 and K2

Thanks for any help in advance.

 

1 word.. Woah!

 

Yeah, haha.

I was able to develop initial conditions after talking with my prof about it after class today.

If you go to this link here: http://forum.allaboutcircuits.com/showthread.php?t=41608

You can see what I came up with for my equations if you're interested. They are attached as PDF's.