  Oscillations in solar prominences are a frequent phenomenon, and they have
been the subject of many studies. A full understanding of the mechanisms that
drive them and their attenuation has not been reached yet. We numerically
investigate the periodicity and damping of transverse and longitudinal
oscillations in a 3D model of a curtain-shaped prominence. We carried out a set
of numerical simulations of vertical, transverse and longitudinal oscillations
with the high-order finite-difference Pencil Code. We solved the ideal
magnetohydrodynamic (MHD) equations for a wide range of parameters, including
the width and density of the prominence, and the magnetic field strength (B) of
the solar corona. We studied the periodicity and attenuation of the induced
oscillations. We found that longitudinal oscillations can be fit with the
pendulum model, whose restoring force is the field aligned component of
gravity, but other mechanisms such as pressure gradients may contribute to the
movement. On the other hand, transverse oscillations are subject to magnetic
forces. The analysis of the parametric survey shows, in agreement with
observational studies, that the oscillation period (P) increases with the
prominence width. For transverse oscillations we obtained that P increases with
density and decreases with B. For longitudinal oscillations we also found that
P increases with density, but there are no variations with B. The attenuation
of transverse oscillations was investigated by analysing the velocity
distribution and computing the Alfv\'en continuum modes. We conclude that
resonant absorption is the mean cause. Damping of longitudinal oscillations is
due to some kind of shear numerical viscosity.
