In this paper, we investigated the dynamic proprieties of one-dimensional system of a classical Brownian particle immersed in a symmetric periodic Remoissenet-Peyrard potential using the Fokker Planck equation. This equation is solved by the Continued fraction expansion method (CFEM). Our results presented for different physical situations, indicated that the dynamical properties are very sensitive to the structure of the Remoissenet-Peyrard potential. Further, we have shown how translational and oscillator motion show up in the dynamic conductivity. Possible applications of this model lie in the field of solid electrolytes and molecular crystals.