In general, dynamic friction coefficient in a dry surface condition is dependent on the relative velocity between two sliding bodies. A conventional method of estimating the velocity dependent dynamic friction coefficient is time consuming and requires a special jig to measure the friction forces. In this paper, a new technique called the state space mapping method is proposed based on the nonlinear dynamics of a 1-DOF friction oscillator. One body is constructed as a single degree of freedom system and another body is formed as a moving base that may be built as a rotating disk or a horizontally oscillating plate. The resulting friction induced vibration system is used to estimate the dynamic friction coefficient. The measured vibration signals are utilized to construct a three dimensional plot of acceleration versus state variables. Then, the velocity dependent dynamic friction coefficient can be estimated from the plot. The natural frequency can also be estimated from the plot, which can be used to verify the quality of the results.