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This paper investigates the numerical solution of a fractionally damped dynamic system. A single degree of freedom spring-mass mechanical system with fractional damping of order 1/2 is considered for the analysis. Homotopy perturbation method (HPM) is used to compute the dynamic responses of the system subjected to unit step and unit impulse loads. Obtained results are depicted in terms of plots. Comparisons are made with the analytic solutions obtained by using fractional green function of Podlubny (1999) [5] and numerical solution of [20,25] in the special cases, to show the effectiveness and validation of the present analysis.