We consider the stability of the equilibrium state of an oscillator with an high natural oscillation frecuency under time-periodic perturbations of the oscillator. It is shown that the problem of stability in the case of general equilibrium can be solved by considering only a linear approximation of the perturbaton. In the singular case a procedure is proposed to construct a nonzero constant, if it exists, whose sign specifies whether the state of equilibrium is asymptotically stable or unstable.