The application of passive control through Tuned Mass Dampers (TMD) has garnered considerable attention in the field of mechanics due to their efficacy in mitigating vibrations in wind turbines. The objective of this study is to demonstrate the significance of incorporating a Tuned Mass Damper (TMD) into the nacelle of an offshore wind turbine subjected to external excitations, particularly aerodynamic and hydrodynamic forces. A mathematical model is developed to formulate the equations of motion for the coupled wind turbine-TMD system. Numerical resolution is conducted using the Newmark method to evaluate the system's vibratory response over time. To determine the parameters of the TMD, a parametric study is performed by adjusting the ratio α, while maintaining the primary parameters of the wind turbine (mass, stiffness, and damping) constant. The focus of this parametric analysis is to examine the impact of variations in the TMD’s mass and stiffness on the structural vibration responses. The findings confirm that the TMD effectively reduces vibrations in offshore wind turbines, thereby enhancing their stability and extending their lifespan. Additionally, it is confirmed that a too low alpha ratio results in insufficient damping, while an excessively high alpha ratio can induce detrimental resonance phenomena.