This research presents the development of a one-dimensional analytical model to investigate the impact of pressure variations in the primary loop on natural circulation (NC). The model takes into account a sinusoidal input heat distribution and derives equations for the parameters of NC. The model covers a broad spectrum of NC patterns, spanning from fully single-phase to fully two-phase flow. The research demonstrates a smooth and continuous transition between various kinds of NC. Moreover, the research demonstrates that NC is capable of efficiently dissipating the decay heat generated inside the core of a pressurized water reactor, encompassing a range from 100% to 60% of the total inventory present within the primary loop. The findings of this study are compared to prior research outcomes and demonstrate a reasonable level of consistency. Additionally, comparisons are made with uniform input power distribution to demonstrate that there are no significant differences in the NC parameters when using sinusoidal heat input.