This paper summarizes numerical studies on free vibration systems with single degree of freedom with tuned pendulum. The model of equation of motion will be derived by Lagrange equation. To get an approximate solution of the model, the Perturbation method will be used to expansive the model. The Runge-Kutta fourth order has been used as the numerical solution. The numerical solution derived model has been verified extensively against exact results, and the results show that the model simulate the dynamic response of free vibration system both with and withouth pendulum is satisfactorily. The pendulum parametric simulation based on Runge-Kutta method shows that length and mass of pendulum that used were influence the amplitude reduction of the dynamic response.