The paper generalizes a notion of the closed orbit for the case when the accelertor lattice is perturbed by a time‐dependent harmonic dipole field. The problem is motivated by effects of current ripple in a proton accelerator. Our result allows to estimate the amplitude of the beam excursions as a function of the amplitude and the frequency of the perturbation. It predicts that the deviation of the beam increases as the frequency of the ripple approaches the sideband betatron frequency.