RC discharge into an LR circuit

tml10

Hello,
I am working on a creating the characteristic equation (in general terms) of the voltage (and current, but not as important) for the capacitor in a RC connected to a LR. The RC circuit is initially charge (say has been connected to a power supply for all time before t = 0) and at t = 0 a switch is flipped and connects the RC to the RL, and allows the RC to do a DC discharge through the RL.

The circuit description in terms of nodes (pSpice convention):
C1 goes from nodes 1 to 0 (0 being ground, and C1 has an initial charge of Vi)
R1 goes from nodes 1 to 2
switch goes from nodes 2 to 3 (and is flipped at t = 0)
L1 goes from nodes 3 to 4
R2 goes from nodes 4 to 0

From simulation with the actual values I know this is an over damped circuit so the form of the equation should look like
V(t) = A₁e^s₁t + A₂e^s₂t
but I don't know if I can say it is a true RLC, or if I have to say it is a RC connected to an RL.

Any help to solve for A₁, A₂, s₁, and s₂ would be very, very helpful. Or telling me what is wrong with my theory would be great too. Thank you in advance!

Travis

p.s. - if you have the time, and are able to help, a walk through of how you obtained the equations would help me understand. Thanks!

p.s.s. - the actual values are as follows
C1 = 1.236 mF
R1 = 50.48 mΩ
L1 = 1.35 μH
R2 = 10.5 mΩ

Carl Pugh

It's been many years and this is not my speciality, but
At t=0
C=1.236 mF
R=60.98
L=1.35μH
Voltage C=Vi
Current=0

Back when I was doing this, didn't use spice, just wrote the equations up in Basic. Results seemed to be correct.