In this study, a system coupled with the nonlinear dynamic vibration absorber was modelled, and its equation of motion was analized by the harmonic balance method to obtain the amplitude ratio. And also, the stability analysis was done by the Routh Hurwitz method. In the vibration systems coupled with the nonlinear dynamic vibration absorber, the unstable region and the jump phenomenon can be ramarkably affected by the damping ratio. The stable and unstable region that obtained to differential method excellently agreed to the result of the stability analysis of Routh Hurwitz.