Friction damping is often used as a vibration isolation medium to protect large objects from vibration. In this paper, it is modeled and analyzed a basis-excited nonlinear vibration system with friction damping using the SCPA method, which is one of the averaging methods. The displacement transmissibility and the stability of the steady state response were analyzed seperately for the linear and the non-linear spring systems. The critical frequency at which the relative motion starts was obtained as a function of the friction ratio, and the characteristics of the displacement transmissibility according to the change of the design parameters were investigated. In the case of the nonlinear spring system, the displacement transmissibilities were divided into three types and the motion characteristics were considered. In particular, there was a peculiarity that the displacement transmissibilty curve was separated at specific parameter values.