Phase lag predicts nonlinear response maxima in liquid-sloshing experiments

Mass-spring models are essential for the description of sloshing resonances in engineering. By experimentally measuring liquid's centre mass a horizontally oscillated rectangular tank, we show that low-amplitude obeys Duffing equation. A bending response curve analogy to softening spring is observed, with growing hysteresis as driving amplitude increases. At large amplitudes, complex wave patterns emerge (including wave-breaking and run up at tank walls), competition between flow states observed dynamics departs progressively from Duffing. We also provide quantitative comparison shapes curves predictions multimodal model based on potential theory (Faltinsen & Timokha 2009) it systematically overestimates amplitudes hysteresis. find phase-lag forcing key predictor nonlinear maxima. The reflects precisely onset deviations - most importantly resonance motion always lags by 90{\deg} (independently pattern). This confirms theoretical 90{\deg}-phase-lag criterion (Cenedese Haller 2020).