Analysis of RLC Circuit v(t): Find Voltage with Ohm's Law

[cheapcheat64]

http://imgur.com/hAzf2zP

So I found the circuit is series, w₀ and a₀ equal 20 so it is critically dampened. For V(inf) I used current divider to get the equation (.1 A *120 ohm)/40 ohm = .3 A. Then I used ohms law to find v(t) = .3*120 = 36 V.

I then wrote down the circuit at t<0, t>0, and t=inf. I am stuck at this point.

 

[donpacino]

so t<0 will give you your initial conditions
t inf will give you your steady state value.
T>0 will give you the differential equation that you are looking for.

write out the differential equation first and solve it, either in time or frequency domains

 

[Hesch]

Your V(inf) calculation is wrong. Substitute the two resistors to the right and the current source with a Thevenin equivalent: 40Ω in series with a 4V voltage source.
So V(inf) = 4V.

The current through the switch, I(0_-) will be (4V - (-6V) ) / ( 40Ω + 40Ω ) = 0.125A (from right to left ).

So V(0_-) = -6V + 0.125A*40Ω = -1V.