We study numerically the varicose dynamics of a forced gravitational liquid sheet (curtain) issuing into a quiescent gaseous ambient. The investigation is performed in supercritical regime, namely for Weber number $We > 1$. Two methodologies are employed: a simplified one-dimensional (1D) linear model and two-dimensional (2D) volume-of-fluid simulations. Using harmonic forcing perturbations of the streamwise velocity applied at the inlet section, the curtain varicose dynamics is excited by varying the forcing frequency $f$ and amplitude $A_u$ of the perturbations for different values of $We$. The 1D analysis reveals that the curtain oscillations amplitude reaches a maximum value for a certain forcing frequency $f=f_{max}$. In other terms, it is found that the flow manifests a resonance behaviour, with the natural oscillation frequency $f_{max}$ and corresponding amplitude $A_{h,max}$ both scaling as $We^\frac{1}{3}$, while the average wavelength $\bar{\lambda}_{max}$ scales as $We^{-\frac{1}{3}}$. It is found that the 2D curtain breaks up numerically by increasing the forcing amplitude $A_u$ in resonance conditions. The numerical rupture is determined by a progressive curtain thinning induced by the varicose deformation, which moves upstream by increasing $We$, i.e. downstream by increasing the surface tension coefficient. In this respect, surface tension is found to play a stabilizing role on the varicose oscillations of the curtain.