Abstract

This study investigates the dynamics of the stochastic pendulum differential equation under the influence of white noise. The equation serves as a key mathematical model to describe physical systems affected by random disturbances. The main objective is to analyze the system’s behavior in response to stochastic perturbations and to examine the impact of key parameters such as damping, noise intensity, and gravity on the stability and motion of the pendulum. To address the stochastic component of the equation, the Wronskian determinant method is employed. This approach enables an analytical solution and provides reliable results under uncertainty. The findings highlight the significant role of random noise in altering the dynamic behavior of the system, offering deeper insights into stochastic systems and nonlinear dynamics.