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Question: Is the circuit which belongs to the quoted text an oscillator?
Note that each oscillator with a feedback loop can also be seen as a negative-resistance oscillator.
In this case, a negative resistance cancels out the positive damping resistances and, thus, allows oscillation.
Example: The oscillator circuit called "Clapp oscillator" shows a negative input resistance at he gate node.
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Second example: WIEN oscillator with fixed gain A=1+Rf/Ro.
Without the grounded resistor R0 the input resistance at the inverting node is Rin=- Rf/2 (at f=fo=1/RC) .
With Ro=+Rf/2 this leads to the well-known oscillation condition with A=1+2=3.
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