The initial aim of this work was the estimation of the lift acting on a flat plate performing small oscillations in a plane uniform stream by means of a simplified model based on one or at the most two lumped vortices, and the assessment of its results by comparison to those that were exact. The model was found to work well up to a reduced frequency of about 1 or 2, above which the results diverged from those that were correct. In order to improve the model, its behaviour at very high frequencies was then investigated, discovering: (i) that if the number of lumped vortices is greater than one the possibility to impose all boundary conditions is subject to certain geometrical constraints; (ii) that the asymptotical behaviour is not the right one. A straightforward extension of this conclusion to the exact case of a continuous, vorticity distribution simulating the motion of the plate and to the classical equation describing it leads apparently to an incorrect result. The reason for the discrepancy is found in the singularity displayed by the integral equation which cannot be reproduced by the discrete model. It this therefore concluded that the latter can be trusted at low and middle frequencies but its extension to higher ones is fundamentally uncorrect.