This paper presents a linearization of the dynamic equation for a free-piston engine generator (FPEG), and simplifies it to a one-degree forced vibration system with viscous damping. The analogy between a massspring damper and a FPEG system is expressed, and the solution to the vibration system is solved. The model was successfully validated with respect to experimental data obtained from a prototype. The simulated piston displacement during steady operation showed similar trends with the test results and the error of the displacement amplitude was controlled within 3%. The state-space equations and the transfer function of the system are obtain using the fast response numerical model. An example of model application in the real FEPG control system was provided. Compared to the previous numerical model with differential approaches, the solving time of the proposed fast response model can be significantly reduced. The simplicity and flexibility of the proposed model make it feasible to be implemented to several computing software, i.e. Matlab, AMESim, Labview, Dymola et al. It can be easily implemented to real-time Hardware-in-the-Loop (HIL) simulation model for the future piston dynamic control system development. In addition, since it reveals how an FPEG operates in a resonant principle, the model is useful for parameter selection in the FPEG design process. (C) 2015 Elsevier Ltd. All rights reserved.