I don't recall a Wien Bridge Osc circuit that doesn't include a non-linear element, seems the gain needs to be adjusted rather finer than a fixed setting.....that's all.
- The trouble with the non-linear elements I mentioned is that they tend to create "bounce" when the frequency is low, (say below 40Hz), since the circuit can "follow" the output amplitude. This causes distortion and makes such circuits unusable below 30Hz (and some may regard 100Hz as the minimum).