Continuous nonlinear transmission lines (NLTLs), also known as gyromagnetic lines, consist of ferrite-based magnetic cores biased by an external magnetic field. Over the past years, many analytical and experimental studies have predicted the rise time reduction of the input pulse to the range of a few nanoseconds or even hundreds of ps experimentally observed in such gyromagnetic lines. This effect, known as pulse sharpening, is investigated in this paper built on a model based on a periodic structure of inductive-capacitive cells in series with magnetization-driven voltage sources expressed by the one-dimensional form (1D) of the Landau-Lifshitz-Gilbert (LLG) gyromagnetic equation. We explore the model through parametric study under various input-pulse parameters to understand the physics behind the ferrimagnetic material responses. Moreover, the numerical results obtained from computational simulations using Mathematica (v. 12.1) show how the line parameters (input voltage, damping constant, saturation magnetization, and length) affect the sharpening effect, which is quantified by the switching time. Our results on ferrite-loaded coaxial lines have confirmed many results found in the literature. We validated with a good agreement the proposed model with the result obtained by Dolan in 1993 using the same 1D form of the LLG equation, thus showing that the model proposed here is suitable to quantify the sharpening effect produced by a gyromagnetic NLTL.