How does positive feedback generates ac waveforms in an opamp?
An op-amp oscillator can be two types usually: -


A squarewave relaxation oscillator when the op-amp is used as a schmitt trigger
A sinewave oscillator where the op-amp is used as a linear amplifier


I'm assuming that the question relates to the 2nd type of oscillator.

To generate a sinewave you need positive feedback to the input. Positive feedback means feeding back a signal that is exactly in phase i.e. op-amp output and op-amp input are in phase exactly. If they are not in phase exactly a sustained oscillation frequency is not achieved.

There are then two more criteria to be met for a sustained sinewave oscillation: -


The feedback has to produce a non-zero degrees phase change for all frequencies except one.
The feedback has to control the sinewave amplitude to prevent the op-amp from clipping i.e. it has to produce the coherent sinwave at just the right amplitude.


It's easy with a squarewave oscillator - you don't mind the op-amp saturating because it won't affect the shape of the squarewave but for a sinewave it can be a little tricky. The circuitry that produces only one coherent frequency is usually a phase shifting network made from resistors and capacitors i.e. it is a filter. Another type of phase shifting network has a specific name - a wein bridge oscillator. This also uses resistors and capacitors.

What ever method is chosen, the result is the same - the signal that gets fed back exactly (and coherently) reinforces the signal at the input to the op-amp amplifier.

Amplitude control is usually based around a circuit element that behaves like a voltage dependent resistor (VDR); the output signal is converted to a dc level representing the amplitude and this is used to reduce the op-amp amplifier's gain via the VDR - if the signal gets too big the gain is reduced thus, the amplitude is kept reasonably constant and free from distortion.