The DART spacecraft will impact Dimorphos, the secondary in the Didymos binary asteroid system, to demonstrate the validity of a kinetic impactor in deflecting a potentially hazardous asteroid. The impact will perturb the binary asteroid’s angular momentum, causing the secondary to begin librating in its orbit. Due to the spin-orbit coupling characteristic of binary asteroid systems, the libration will have an effect on Dimorphos’s orbit, causing the orbit period to fluctuate over time. The non-constant orbit period is driven by two modes, a short-period and a long-period, each with significant amplitudes on the order of tens of seconds and periods on the order of days and months, respectively. Impacts with a larger angular momentum transfer result in a larger libration amplitude and greater variations in the non-constant orbit period. Furthermore, the post-impact dynamics are also dependent on the size of Dimorphos and the initial configuration of the binary system relative to a synchronous equilibrium. The non-constant orbit period offers both a challenge and an opportunity to the DART mission: the oscillations will make measuring the orbit period to a high degree of accuracy more difficult, but can help constrain the libration state and momentum transfer of the impact.