Autoparametric Resonance in Two Systems: From the Spring–Pendulum to a T–Shaped Screw in Microgravity

Autoparametric resonance describes energy transfer between coupled modes when system parameters drift slowly through resonance conditions. This paper presents a unified interpretation of two seemingly unrelated systems — the vertical spring–pendulum and a freely rotating T-shaped screw in microgravity — by framing both as slow–fast dynamical systems governed by a decaying frequency mismatch Δf(t). Within USP Field Theory, Δf is interpreted as a resonance corridor mismatch, and resonance occurs when this mismatch crosses a narrow critical band. The framework leads to explicit experimental diagnostics, falsifiable predictions, and a geometric interpretation of mode activation that is consistent with classical mechanics. The work is self-contained and intended as a testable, minimal resonance framework bridging classical dynamics and geometric field interpretation.