A gravitational liquid jet (curtain) issuing into a quiescent gaseous ambient and subjected to varicose perturbations is numerically investigated in this work. The study is relevant for technological applications such as coating deposition, where varicose perturbations of the curtain interfaces can arise due to velocity fluctuations coming from the delivering pump placed upstream of the coating die. The investigation is performed in a supercritical regime, namely for Weber number We > 1. Two methodologies are employed: a simplified one-dimensional linear model, and two-dimensional volume-of-fluid simulations. Using harmonic forcing perturbations of the streamwise velocity applied at the inlet section, the curtain varicose dynamics is excited and characterized by varying the forcing frequency f and amplitude Au of the perturbations for different values of We. As a significant result, the one-dimensional linear analysis reveals that the curtain oscillations amplitude reaches a maximum value for a forcing frequency. In other terms, it is found that the flow manifests a resonance behavior, with the natural oscillation frequency and corresponding amplitude Amax both scaling as We^(1/3), while the average wavelength scales as We^(-1/3) . The two-dimensional volume-of-fluid simulations confirm the one-dimensional model predictions of the flow natural frequency. Moreover, it is found that the curtain breaks up by increasing the forcing amplitude Au. The curtain rupture is determined by a progressive thinning induced by the varicose deformation, and it occurs at a specific value of the forcing amplitude, which does not depend on the Weber number. Along with previous studies of literature regarding the sinuous dynamics of curtain flows, this work represents a further step towards the derivation of a weakly nonlinear physical model accounting for the coupling between sinuous and varicose modes in gravitational liquid jets.