The effectiveness of the viscously damped vibration absorber is presented for the case in which the magnitude of the periodic exciting force acting upon the main system is proportional to the square of its frequency. Dimensionless expressions for the amplitudes of the main mass and absorber mass and for their phase relationships are derived as functions of frequency for three cases, namely, one in which the absorber is tuned to the natural frequency of the main system, one in which the absorber is tuned for maximum effectiveness over a wide range of forcing frequencies, and one in which the absorber is coupled to the main system by a viscous fluid only (the viscous Lanchester damper). The influence of main-system damping upon the amplitude of vibration of the main mass is shown for each case. Diagrams are presented showing the optimum damping, the maximum amplitude of the main mass, and the maximum relative amplitude between the main mass and absorber mass, as functions of the mass ratio. The performance of the absorber when applied to the system having velocity-squared excitation is compared with its performance when applied to the system having constant exciting force, published previously (1, 2). The tuning and damping for optimum performance are found to be different in the two cases. A model absorber with controllable tuning and damping, constructed for experimental work, is described and experimental data are presented for the case of most favorable tuning.