In this paper, we consider some mean-kiadratic and almost known stable and non-linear oscillators under the influence of random parametric excitation in the form of broadband Gaussian white noise of low intensity and correlation time. It is known that applying the Khasminsky averaging method to the stochastic differential equation of the oscillator yields the stochastic differential equation of Ito. The averaged amplitude, as a solution to this differential equation, is estimated using the method of comparison with the solution of some linear stochastic differential Itô equation.