Main purpose of this paper is to analyse the forced vibration prevention of the vibration system with positive or negative damping by the damped dynamic absorber. The cases treated in this paper are: the case I (the alternative exciting force of a constant magnitude is acting on the mass of the main system), the case II (the alternative exciting force, of which the magnitude is proportional to the square of its frequency, is acting on the mass of the main system), and the case III (the alternative displacement is given to the foundation of main system), It is explained how the spring constant and the damping factor of the dynamic absorber are desirably optimized to make the vibration effect minimum. The optimum values in the above cases are given by the convenient empirical formulae.