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Dynamic equation of a simply supported beam with a lump mass in the midspan subjected to harmonic axial excitation, whose one end can move along the beam freely, is a nonlinear differential equation with no explicite solution. In this article we start extracting the equation of motion. Existence of periodic solution, under some condition, are investigated and proved using green function and Schaunder’s fixed point theorem; also noting into the structure of differential equation of motion, existence of oscillating response investigated, independently. By this analysis, it becomes possible to predict whether the solution converges to a point (zero) or a periodic answer.