The development of eccentric-mode resonances in accretion discs within binary systems is simulated. The measured rotational rates of the resulting eccentric discs are found to agree with the observed superhump periods of SU UMa stars. This lends support to the eccentric-disc model of superhump formation. In addition, the decline of the superhump period is found to be explained by the inwards propagation of the eccentric mode. Measurements of superhump periods therefore constrain both the mass ratio of a system and the structure of its accretion disc.