I’m not quite sure what you mean by a Fedchenko drive exactly. If his drive suffered from vibration it certainly didn’t stop it being the most precise pendulum clock made in series production, being clearly able to detect tidal g variations. Fedchenko’s magnet and coil arrangement is tricky to make but gave a very clean unidirectional impulse in the direction of pendulum motion.
There’s a class of clocks that have an axially mounted magnet on the end of the rod swinging over a coil, which might be what you are referring to, in the fashion described in the link I gave. I’ve made a couple of these, vibration wasn’t a significant problem with either. Perhaps because only a very small impulse is needed. Generally they apply the impulse by repulsion just after BDC and usually use the voltage pulse induced in the coil to sense position, as did Fedchenko’s mk2 clock.
Synchronome clocks have a very hammer-like impulse and lots of resulting rod vibration but nevertheless can be very accurate.
In my limited experience of AI it usually gives uninformed and misconceived anwers to horological questions.
I know of 3 people who have made successful sinusoidal drive clocks. I don’t see how this could be applied to a Fedchenko drive, please explain.