Results of the parametric study of transverse oscillations. Top left: displacement of centre of mass as a function of time from simulations with n = 1 and with χ = 5 (black crosses), χ = 10 (green asterisks), χ = 20 (light blue diamonds), χ = 50 (dark blue triangles), and χ = 100 (red squares). Top right: oscillation period as a function of the density contrast, χ. Bottom left: damping time as a function of χ. Bottom right: ratio of damping time to period as a function of χ. In the top left panel, solid lines represent fits of the numerical results. In the remaining panels, the black solid and dashed lines correspond to the results obtained by solving the 2D eigenvalue problem for n = 1 and n = 2, respectively. Symbols represent the results from the simulations. For n = 1, P_ref = P₀; for n = 2, P_ref = P₁.