Can You Solve This Circuit with Mutual Inductance and Capacitance?

[Slightly]

Homework Statement

In the given picture, I need to formulate some kind of solution to find functions for the current, knowing that the two inductances create a mutual inductance (coupling)

The Attempt at a Solution

I start by formulating these two equations where M is the mutual inductance.

For the left, E= Q/C + L₁*dI₁/dt - M*dI₂/dt
and
for the right, 0= L₂*dI₂/dt + R*I₂ - M*dI₁/dt

Does this look okay so far, and where should I go from here?

 

[darkxponent]

What is Q?. Find it and the question will be solved.

 

[Slightly]

Q is just the charge on the capacitor

 

[darkxponent]

Is there a relation between Q and I1, I2 ?

 

[Slightly]

I'm sure there is one, but Q is just a characteristic of the capacitor.

 

[darkxponent]

I'm sure there is one, but Q is just a characteristic of the capacitor.

The two equations you have made have 3 variables(Q ,I1, I2,) so it can't be solved. Try to get a third equation and you will have 3 equations for three variables.

Hint: The third equation is a relation between I1 and Q. What is it?