This paper induces the reduction factor of the total input energy due to the damping in the elastic single-mass system on the basis of the equilibrium of the total input energy to the system. In the induction of , the paper defines the fundamental formula at the nonstationary response based on the theoretical reduction formula at the stationary response, and gives the coefficient of the formula by analytical response results. Finally, the paper indicates the conformity of the proposal of the evaluation formula of by comparing with analytical response results.