the outrigger is one of the effective systems for lateral displacement mitigation in tall buildings. by using linear viscous dampers and investigation the perimeter columns stiffness, a novel damped outrigger system, has been proposed. in this paper, to gain insight into preliminary specifications of such systems, like damping and outrigger's optimum location, two simplified models including, beam-damper and beam-spring-damper, has been developed. two partial differential equations governing the motion of each models assuming a Bernoulli-Euler beam. a closed-form analytical solution is developed. by applying appropriate boundary conditions (for displacement and force), at the end, the multiplier matrix and charactristics equation is obtained. The complex natural frequencies related to the corresponding non dimentional parameters including, damping and outrigger location, has been obtained by solving charactristics equation with numerical method. The result for damping ratio respected to damping and outrigger location, has been shown with curves which the optimal location and damping for each mode was obvious.