Context. 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, however. Aims. We numerically investigate the periodicity and damping of transverse and longitudinal oscillations in a 3D model of a curtain-shaped prominence. Methods. 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 (wx) and density (ρp0) of the prominence, and the magnetic field strength (B) of the solar corona. We studied the periodicity and attenuation of the induced oscillations. Results. We found that longitudinal oscillations can be fit with the pendulum model, whose restoring force is the fieldaligned 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 ρp0, but there are no variations with B. The attenuation of transverse oscillations was investigated by analysing the velocity distribution and computing the Alfvén continuum modes. We conclude that resonant absorption is the mean cause. Damping of longitudinal oscillations is due to some kind of shear numerical viscosity. Conclusions. Our model is a good approximation of a prominence body that nearly reproduces the observed oscillations. However, more realistic simulations that include other terms such as non-adiabatic processes or partially ionised plasmas are necessary to obtain better results.

Context. Prominence threads are dense and cold structures lying on curved magnetic fields that can be suspended in the solar atmosphere against gravity. Aims. The gravitational stability of threads, in the absence of non-ideal effects, is comprehensively investigated in the present work by means of an elementary but effective model. Methods. Based on purely hydrodynamic equations in one spatial dimension and applying line-tying conditions at the footpoints of the magnetic field lines, we derive analytical expressions for the different feasible equilibria (se) and the corresponding frequencies of oscillation (ω). Results. We find that the system allows for stable and unstable equilibrium solutions subject to the initial position of the thread (s0), its density contrast (ρt) and length (lt), and the total length of the magnetic field lines (L). The transition between the two types of solutions is produced at specific bifurcation points that have been determined analytically in some particular cases. When the thread is initially at the top of the concave magnetic field, that is at the apex, we find a supercritical pitchfork bifurcation, while for a shifted initial thread position with respect to this point the symmetry is broken and the system is characterised by an S-shaped bifurcation. Conclusions. The plain results presented in this paper shed new light on the behaviour of threads in curved magnetic fields under the presence of gravity and help to interpret more complex numerical magnetohydrodynamics simulations about similar structures.