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