Translations with piecewise cubic trajectories are studied in the frequency domain. This class of motion has as an important subcase: cubic spline trajectories. Translations with trajectories depending on time with general polynomial law are preliminarily considered, and a general theorem concerning this type of motion is introduced. The application of this theorem to the case of cubic time dependence and the consideration of finite-duration effects lead to the solution of the piecewise cubic trajectory case. The results, which are remarkably different from those concerning constant velocity translations, clearly indicate the importance of the role of velocity and time duration. In this respect, they confirm the validity of constant velocity motion as a first-order model for frequency domain analysis of motion.>