Sallen-Key Low Pass Oscillator
G36 gave you good advice. If you set \$\zeta=0\$, you have infinite \$Q\$. And doing so also sets the voltage gain of a Sallen Key LP filter to \$A_v=3\$.

Here's the simple template:







simulate this circuit &ndash; Schematic created using CircuitLab

As shown, I've set the values of \$R_1\$, \$R_2\$, \$C_1\$, and \$C_2\$ to provide about \$1\:\text{kHz}\$ for the corner frequency. You can adjust them as you see fit. Just make sure that \$R_4\$ is more than twice the value of \$R_3\$ to achieve oscillation. (Exactly twice the value sets \$A_v=3\$. But you want just a little more than that, I think.) \$C_3\$ is required to compensate the opamp and avoid very high frequency (unwanted) oscillations.

The output won't be a perfect sine wave, though. But you can always filter the output more, if you want. Just paste another two-pole Sallen Key filter at the output with the same corner frequency, perhaps:







simulate this circuit

I'm just shooting from the hip. But that's the basic approach.