Small oscillation…?

We defined a small oscillation as an oscillation involving small displacement $x$ (or $\theta$, small angular displacement). However, we know that a dimension-ful quantity cannot be said to be small or large without comparing it to a reference quantity. What would be that reference quantity for $x$, here?

1. A characteristic length scale of the potential energy, U(x).
2. The maximum amplitude of the simple harmonic motion.
3. The spatial resolution of the experiment involved.