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This paper aims to investigate the behavior of a spherical absorber composed of two parts, an inner sphere and a supporting convex spherical dish in which the ball is placed. Considering only the planar behavior of the system, a set of governing nonlinear differential equations was derived and solved numerically. Firstly, the system is exposed to the harmonic excitation of the supporting bowl and its time response is analyzed for all time dependent variables. By gradually changing the angular frequency of the excitation, a resonance curve is obtained, which is examined in detail with respect to the changing amplitudes of the excitation force and the nonlinear behavior. The effect of internal damping and different settings of the absorber characteristics are also investigated. The effect of initial conditions without the presence of an external excitation force is also numerically analyzed by means of phase portraits for selected pairs of initial conditions. [ABSTRACT FROM AUTHOR]