Damping algorithm explained in figures. Vertical lines indicate (integer multiples/divisors of) the mean motion (solid) and all three normal modes: longitudinal (dotted), latitudinal (dashed) and wobble (dash-dot-dot). Panel a: Comparison between damped and undamped tidal librations. Panel b: Frequency content of Phobos-fixed longitude of Mars for both the damped and undamped dynamics. Panel c: Frequency content of Phobos-fixed latitude of Mars for both the damped and undamped dynamics. Panel d: Damping process of the latitudinal librations close to the latitudinal normal mode.