The horological community principally uses two methods to find the amplitude of a pendulum -- one is an obvious use of the work energy theorem. i.e. measure the speed at the equilibrium position (Bottom Dead Centre), the other the time the pendulum is "beyond" the photogate placed near the maximum displacement. This method is claimed to be more sensitive and a more direct measure of the amplitude (It's been compared to visual measurements.)
These methods are however discrepant when a magnetic field is used to simulate a changed g, i.e. to imitate the changing g due to the relative position of the moon.
Unfortunately, one cannot use a space constant magnetic field to change the force on a pendulum with a bob containing a PM. This, I surmise, is why the measurements differ. The time beyond the photogate requires pendulum sinusoidal motion and the W-E method requires a high Q. (The pendulum must not lose much energy during a single half cycle.) Neither occur using this simulation method. The displacement is not sinusoidal because the force is not constant, and I think the Q is reduced by the magnetic method, because of eddy currents, and the Faraday effect in the coil driven by a low Z source.