The context is explained in this post: What is the reason for the orbital movement of the Foucault pendulum?
But now my question is not about the orbital behaviour of the pendulum.
I wonder if the amazing fact that the plane of swing (PS) doesn't rotate with the Earth depends on the amplitude of oscillation.
I think it is reasonable to assume that if the pendulum is not oscillating at all, the mass at the bottom will rotate with the earth as any other object around.
On the other hand, for an amplitude of 2m, PS doesn't rotate along the Earth, and therefore moves for an local observer.
And for 1m, 0.5m, 0.25m ...?
If we suppose that the time for a complete rotation of PS depends only on the latitude, (what results in 31.8 h in Paris for example), and not on the amplitude, is there a sudden discontinuous point at zero?
But if that time is a function of latitude and amplitude, which function is that?