The present paper deals with the fluid forces induced by a rapidly moving rigid circular cylinder in an incompressible fluid initially at rest. The cylinder is subjected to an impulsive motion which corresponds to unique sinusoidal period of acceleration and is then stopped. Two fluid domains are considered: infinite and cylindrically confined. This study focuses on small displacements of the cylinder in regards to its radius, i.e. for low Keulegan-Carpenter numbers. In a first part, the flow is assumed potential. Only the inner cylinder is displaced and the outer one, in the confined case, is at rest. The problem, formulated as a two-dimensional boundary-perturbation problem, is solved thanks to a regular expansion. A non-linear analytical formulation of the fluid forces experienced by the moving cylinder is then proposed. Its range of validity is discussed with regards to the inner cylinder displacement. The results are confronted to numerical simulations with a CFD code based on a finite volume discretization on a moving mesh. In a second part, a two-dimensional viscous flow is considered. Analytical formulations of the fluid forces experienced by the cylinder subjected to arbitrary motions are proposed. The starting point of the analytical approach is the fluid forces expressions obtained with harmonic motion. These expressions come from the Rosenhead model for the infinite fluid domain. A Fourier transform is applied on the harmonic solutions to capture the wide frequency spectrum composing the transient motion. An inverse Fourier transform is then applied on the resulting expressions to derive the solutions in the temporal space. The analytical solutions are discussed and compared to numerical simulation results obtained in an infinite domain for various Stokes numbers. The competition between the viscous diffusion time and the wave duration time is studied which allows to underline history effects on the force.

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