We study the motion which results when a fluid film is squeezed between two parallel surfaces in relative motion.  Particular attention is given to the special case where one surface is fixed and the other is impulsively accelerated from a state of rest to a state of sinusoidal oscillations in a direction normal to its plane. In addition to the presentation of analytic solutions which are based on the regular perturbation technique and on the linearised analysis of the resulting nonlinear partial differential equation, a numerical solution of the full nonlinear equation based on a finite-difference scheme is obtained. The effects of the sinusoidal motion on the velocity profiles and on the normal forces which the fluid exerts on the surfaces are investigated.