= Controls and limitations of a Foucault pendulum
{c}
An unwanted <ellipse> is an experimental warning: a finite-amplitude pendulum can develop additional orbit-axis <precession> even without <Earth's rotation>. A symmetrical, firm support and careful launch reduce this effect.<Foucault's pendulum - the physics (and maths) explained by Joe Wolfe>[Foucault's pendulum - the physics (and maths) explained, Complications: finite elliptical motion and asymmetries in support, launch, and drag]{ref} Distinguish that nonlinear effect from the tiny <ellipse> already present in the <Exact linear Foucault pendulum trajectory>. The linear calculation establishes a controlled approximation, not the complete motion of an arbitrary large swing.
Support <anisotropy> creates a second competing mechanism. As an illustrative modification, let the two horizontal restoring <angular frequencies> be $\omega_x$ and $\omega_y$. Even with $\alpha=0$, a diagonal release from rest gives
$$
x=A_x\cos\omega_xt,\qquad y=A_y\cos\omega_yt.
$$
When $\omega_x\ne\omega_y$, the relative <phase> changes on the scale $1/|\omega_x-\omega_y|$: the trace changes shape without any terrestrial <Coriolis force>. It need not be uniform <precession> of a <Foucault pendulum>. To cleanly resolve the terrestrial effect over times of order $1/|\alpha|$, a useful design target is $|\omega_x-\omega_y|\ll|\alpha|$. Near the equator that target becomes particularly demanding. Compare fast periods along perpendicular launch directions to look for this frequency splitting; repeat at several launch orientations to detect preferred suspension axes.
Other controls address distinct alternatives: shelter the apparatus from air currents, track the support against the building, measure both orbit axes, and compare early and late fitted directions as the <amplitude> decays. A sustaining drive, if used in a different apparatus, must supply <mechanical energy> without imposing an azimuthal bias; an undriven run provides a useful comparison. A change in swing direction alone cannot exclude these effects. Agreement of the signed rate with independently known <geographical latitude> and <Earth's rotation>, together with stable repeat launches and small competing effects, is the inference the experiment is designed to support.
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