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System identification (SI) is a modeling method using experimental input-output signals without any physical properties of the system. In this study, a flexible planar manipulator is modeled with the SI method. The output is an acceleration signal of the tip point of the manipulator and the inputs are triangle and trapezoidal motion profiles. Motion parameters are set in order to reduce residual vibrations of the flexible manipulator. The mathematical model of the system is estimated with the continuous-time SI method. Simulation results are obtained by using the mathematical model. The identification and validation data are successfully matched with the experimental results.