In a shear flow, a small sphere may experience a lift force due to fluid inertia. Most previous workers assumed that the particle was stationary so that they could treat the fluid motion as steady. In spite of this, the results of previous analyses have generally been applied to problems in which particles move in an unsteady fashion. This paper presents the results of singular perturbation calculations of the lift on a sphere in a linear shear flow. The velocity of the sphere oscillates sinusoidally in time. Although the problem is idealized, the results provide some physical understanding of the effects of unsteadiness and the frequency regime in which one may assume quasisteady conditions.