Op Amp based Hartley oscillator

Build an oscillator that will satisfy a few requirements. The main requirement is to have exactly one capacitor. Another one is to have high Q and sine wave output. I am considering Hartley`s oscillator design. Since it has only one cap. I don`t what to built the biasing network and select a transistor that will suit the oscillator`s needs, so I figured that there
Op Amp based Hartley oscillator - schematic

must be a way to build Hartley`s oscillator around an operational amplifier as shown on the figure below. I have made the simulation as shown above, and I believe it should oscillate, since the gain of the Op Amp negative feedback loop is greater than $frac{L1}{L2}$ ratio. But the oscillations start and die. I can see that the frequency of the decaying oscillations is correct, but they would not sustain. I event tried to crack the gain up to some unreasonable number, but this doesn`t help at all.

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