I thought is was explained that the circuit apparently does not perform a linear function,

I mean that why the circuit is not linear, that V+ is not equal to V- (Op amp inputs). I've sent some equations. But it happened that the Op amp is linear but I quess we made a mistake but I don't know where.

 

Me and my teacher made some calculations and it turned out like this :

View attachment 262929

I don't know where we made an error here.
Because it shows that the Op amp is linear. But of course we know it's not but where is the error?

I want to show that the positive feedback is stronger and nothing can change it.

Your error is that it is not linear. You cannot analyse in the frequency domain. The only analysis that works on this circuit would be in the time domain.

 

Your error is that it is not linear. You cannot analyse in the frequency domain. The only analysis that works on this circuit would be in the time domain.

Well if it's not linear then the equation should have conflict. And if there is a conflict with Kirchhoff's law then V+ is not equal to V- so it should work but it doesn't.

 

Well if it's not linear then the equation should have conflict.

You are analysing it as though it is a sinewave. It isn't.

 

Well if it's not linear then the equation should have conflict. And if there is a conflict with Kirchhoff's law then V+ is not equal to V- so it should work but it doesn't.

Yes - there is a conflict:
The input signal is connected to the inverting terminal. However, the closed-loop gain expression is positive - and has a pole with a positive real part.
By the way: Even for instable systems we can compute a transfer function (even a simulation program can do this) - but it does not reflect the real behaviour; we cannot measure it. However, it has some value for theoretical analyses.
Indication for instability: (1) Pole with a positive real part and (2) A rising phase response caused by the denominator

 

I don't know where we made an error here.

a closest (quick found) similar circuit DOI: 10.1177/1077546315585424
The fact that the C has a remnant integrated charge (performs the integrating function)
and acts in differential time slice as a dc voltage source with it's ESR as an internal resistance
so . . . along with your ac source it strictly drives the inverting input to V.source.ac + V.capacitor
. . . not necessarily to the U.out / 2 ← is where the op amp attempts to balance itself AND is not
what instantly occurs at any combination of the input voltages

moreover if the electrolytic 10uF capacitor is used it's capacity is dependent on it's terminals polarity (the least adds yet another non-linearity option to the circuit)

 

Well if it's not linear then the equation should have conflict.

Not necessarily.
A linear equation assumes the system is linear.
It doesn't tell you if it's nonlinear, since the equation doesn't know that.
The op amp may be linear, but it's operating in a non-linear circuit.
Equations only work if they are describing the actual system operation.