Nowadays, many global efforts have been devoted to developing renewable energy sources to mitigate the climate impact of the conventional fossil-based energies. The use of wind energy has increased in recent years, and also the necessity of proposing effective maintenance for such devices. With the aim of understanding the dynamic behavior and vibrational characteristics of the drive-train in wind turbines, to help the condition-based fault analysis, the proposal of useful dynamical models is well received by the maintenance community for research and educational purposes. In this paper, a simple yet realistic mathematical model to analyze the dynamic behavior of the drive-train of a wind turbine is presented. The model focuses the analysis on the third stage of the gearbox-based multiplier by taking into account diverse physical phenomenons as the vibration sources, including time-varying mesh stiffness, time-varying viscous damping, transmission error, and backlash. Dynamic analysis was carried out to investigate the behavior of the system under a torque obtained from a convincing wind speed.