An analytic method for predicting the spectral character of vibrations generated by an important class of defects in ball bearings is described. This family of bearing problems comprises those operating modes in which the magnitude of the ball-race contact force varies continuously and periodically as the bearing rotates. Defects of this type include race misalignment and off-sized rolling elements. The analytic technique is based on solving Lagrangian equations for the time-varying displacement of the bearing race in response to the rotating system of ball forces.