This paper presents a mathematical analysis of the action of a dynamic vibration absorber. The system analyzed consists of a main mass attached to a rigid foundation by a linear spring coupled to the absorber mass by a spring of nonlinear characteristics. The forced oscillations of the system produced by a harmonic disturbing force acting on the main mass are studied analytically. It is assumed that the coupling absorber spring has nonlinear force-displacement characteristics of the hyperbolic sine type. Expressions for the amplitudes of the vibrations of the two masses as functions of the frequency of the disturbing force are obtained.