Mutual Inductance Problem: Find V(t)

[bobbyw]

This problem is tougher than I though and I'm stuck on a couple of things.

Homework Statement

There are 2 inductors, a DC power source, 2 resistors, and a switch. The circuit looks just like the image I've attached, except it will have a switch on the left of the first resistor and the values are different. sorry about that.
The DC source is 12V
The inductors are 4H, and 16H, respectively (L₁ and L₂).
The resistors are 12Ω and 48Ω, respectively(R₁ and R₂).
K=1
The switch is open for a long period of time previous to t=0 (inductors fluxed), and opened at t=0.
The problem is to find V_out(t). In the image attached, V_out would be the voltage across R₂.

Homework Equations

K=M/sqrt(L1*L2). since K is given as 1, M is sqrt(L1*L2), which is 8H.

The Attempt at a Solution

I initially set up the loops using KVL. For the left hand side of the circuit I got:
12 = (12+s4)I₁ - 8sI₂

and for the right:
0 = -8I₁ + (48+s16)I₂

from this, the system determinant can be found, and I₂ can then be found.
I am stuck right now is the switch though.
for finding V(t<0), the inductors are fluxed, thus acting as short circuits. Does this mean that the mutual inductance will come into play or can be neglected? I have thought of a couple different possibilities.
V(t<0) = 0 because the inductors are not electrically connected and no current is flowing?
V(t<0) = 12 because the inductors are acting as short circuits, and the mutual inductance will appear to be a short circuit as well, making the voltage on the left and right side of the circuit the same?
V(t<0) = a voltage divider between the two resistors if the above ^ applies?

I also need to find to V(t>=0) but the questions above should help me with that.


Thanks in advance for any help.

 

[jegues]

The switch is open for a long period of time previous to t=0 (inductors fluxed), and opened at t=0.
The problem is to find Vout(t). In the image attached, Vout would be the voltage across R2.

Do you mean its closed at t=0?

V(t<0) = 0 because the inductors are not electrically connected and no current is flowing?

I think this is the case we're dealing with, hopefully another member can confirm my suspicions.

 

[bobbyw]

Do you mean its closed at t=0?

Sorry about that, i meant the switch is CLOSED previous to t=0 for a long time, making the inductors fully fluxed. really all of the cases make sense to me, and I've been searching for a definitive answer but haven't found one. thanks for the opinion.

 

[jegues]

Sorry about that, i meant the switch is CLOSED previous to t=0 for a long time, making the inductors fully fluxed.


really all of the cases make sense to me, and I've been searching for a definitive answer but haven't found one. thanks for the opinion.

My answer is going to change now based on how you clarified the question. Let me think about it and I will get back to you.