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This is not a Wein bridge oscillator, though it's trying a bit to look like one.

I've redrawn it slightly, to emphasise the 'Wein' components R6, C2 in series and C1 and R1 in parallel to ground. This schematic is drawn with LTSpice. The reference designators are the same as those in the question.

So it's not behaving like a Wein Bridge oscillator with a linear dependence on tuning resistance, it's going as the square root of R. The circuit appears to be behaving as if it's synthesising an LC, with the value of one of them linearly related to the tuning resistance. It's an interesting circuit though. As R1 needs to swing over such a wide range, it's of limited usefulness. I'd be inclined to use a state variable oscillator if I needed a wide range oscillator and could afford multiple opamps.

This is not a Wien bridge oscillator, though it's trying a bit to look like one.

I've redrawn it slightly, to emphasise the 'Wien' components R6, C2 in series and C1 and R1 in parallel to ground. This schematic is drawn with LTSpice. The reference designators are the same as those in the question.

So it's not behaving like a Wien Bridge oscillator with a linear dependence on tuning resistance, it's going as the square root of R. The circuit appears to be behaving as if it's synthesising an LC, with the value of one of them linearly related to the tuning resistance. It's an interesting circuit though. As R1 needs to swing over such a wide range, it's of limited usefulness. I'd be inclined to use a state variable oscillator if I needed a wide range oscillator and could afford multiple opamps.

I've redrawn it slightly, to emphasise the 'Wein' components R6, C2 in series and C1 and R1 in parallel to ground. This schematic is from LTSpice.

That's as far as I'm going to go with a verbal description. It needs somebody to do nodal analysis and write down the phase shifts and amplitudes to demonstrate that there is a resonant frequency where all the phase shifts are zero and the gains unity.

I've included my LTSpice file below for your simulating convenience.

I've redrawn it slightly, to emphasise the 'Wein' components R6, C2 in series and C1 and R1 in parallel to ground. This schematic is drawn with LTSpice. The reference designators are the same as those in the question.

That's as far as I'm going to go with a verbal description. It needs somebody to do nodal analysis and write down the phase shifts and amplitudes to demonstrate that there is a resonant frequency where the gain round the loop is unity with zero phase shift.

I've included my LTSpice .asc file below for your simulating convenience.

U1 with R2 is a virtual ground amplifier, presenting a short circuit to the bottom of R1. It's a transconductance amplifier with a gain of R2, producing a voltage at its output of 100k x -I(R1).

U2 is a differential amplifier, with inputs from both V(mid_point), and U1. They can be taken separately by fixing the other, and then superposing the two results.

With U1 output fixed, the output of U2 is 2 x V(mid_point)

It seems to me that the V(midpoint) and I(R1) will always be in phase. It appears that it's the phase shift through R6 and C2 changing that controls the resonant frequency.

So it's not behaving like a Wein Bridge oscillator with a linear dependence on tuning resistance, it's going as the square root of R. The circuit appears to be behaving as if it's synthesising an LC, with the value of one of them linearly related to the tuning resistance. It's an interesting circuit though.

U1 with R2 is a virtual ground amplifier, presenting a short circuit to the bottom of R1. It's a transconductance amplifier with a gain of R2, producing a voltage at its output of 100k x -I(R1). It's basically measuring the current in R1.

U2 is a differential amplifier, with inputs from both V(mid_point), and U1. It can be analysed by fixing one input, computing the gain for the other, and then superposing the two results.

With U1 output fixed, the output of U2 is 2 x V(mid_point).

It seems to me that the V(midpoint) and I(R1) will always be in phase. It appears that it's the phase shift through R6 and C2 into the C1/R1 load that controls the resonant frequency.

So it's not behaving like a Wein Bridge oscillator with a linear dependence on tuning resistance, it's going as the square root of R. The circuit appears to be behaving as if it's synthesising an LC, with the value of one of them linearly related to the tuning resistance. It's an interesting circuit though. As R1 needs to swing over such a wide range, it's of limited usefulness. I'd be inclined to use a state variable oscillator if I needed a wide range oscillator and could afford multiple opamps.