I'm studying for electronics, but I'm lost with this exercise.

Consider the following oscillator in the picture.

The AMPOP is not ideal: Rin=1k, Rout=1.
How do I determine the minimal voltage gain Av in order for the circuit to function?

Also, the RMS current that feeds the AMPOP is 4mA.
Ignoring the small internal loss of the amplifier, how do I define the oscillation amplitude at the terminals of the LC section?

 

You do not show an oscillator circuit.
Instead you show an opamp that is biased wrong because both its inputs are at ground so its output will also be at ground.

If the opamp is biased at half the supply voltage or has an additional negative supply voltage then its output will be a saturated square-wave with an amplitude that is detailed in its datasheet.

 

This is really a poor quality OPAMP for exercising.
I suppose the purpose is to understand the effect of the intrinsic "imperfection".

Also, I think the OPAMP here is implementing a negative impedance, to compensate for the energy loss of the LC circuit.
This because in reality the LC section behaves as C//L//R, and so the oscillation get smaller and smaller until all the energy has dissipated.

This is a theoretical problem given to me as it is.
I'm trying to solve this as a personal study, but I don't know how to.