The nonlinear decay of oscillations of a liquid column in a U-shaped tube is investigated within the theoretical framework of the projection method formalized by Bongarzone et al. [Chaos 31, 123124 (2021)]. Starting from the full hydrodynamic system supplemented by a phenomenological contact line model, this physics -inspired method uses successive linear eigenmode projections to simulate the relaxation dynamics of liquid oscillations in the presence of sliding triple lines. Each projection is shown to eventually induce a rapid loss of total energy in the liquid motion, thus contributing to its nonlinear damping. A thorough quantitative comparison with experiments by Dollet et al. [Phys. Rev. Lett. 124, 104502 (2020)] demonstrates that, in contradistinction with their simplistic one -degree -of -freedom model, the present approach not only describes well the transient stick -slip dynamics, but also correctly captures the global stick -slip to stick transition, as well as the residual exponentially decaying bulk motion following the arrest of the contact line, which has been so far overlooked by existing theoretical analyses but is clearly attested experimentally. This study offers a further contribution to rationalizing the impact of contact angle hysteresis and its associated solidlike friction on the decay of liquid oscillations in the presence of sliding triple lines.