In this paper, we first analyze a parametric oscillator with both mass and frequency time-dependent. We show that the evolution operator can be obtained from the evolution operator of another parametric oscillator with a constant mass and time-dependent frequency followed by a time transformation\documentclass[12pt]{minimal}
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				\begin{document}$$t\rightarrow \int _0^t dt'\,1/m(t')$$\end{document}t→∫0tdt′1/m(t′). Then we proceed by investigating the quantum dynamics of a parametric oscillator with unit mass and time-dependent frequency in a Kerr medium under the influence of a time-dependent force along the motion of the oscillator. The quantum dynamics of the time-dependent oscillator is analyzed from both analytical and numerical points of view in two main regimes: (i) small Kerr parameter\documentclass[12pt]{minimal}
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				\begin{document}$$\chi $$\end{document}χ, and (ii) small confinement parameterk. In the following, to investigate the characteristics and statistical properties of the generated states, we calculate the autocorrelation function, the MandelQparameter, and the HusimiQ-function.