A nonlinear energy sink is designed to control the oscillations of a two degreesof-freedom pendulum under the following types of excitations: horizontal and vertical base displacements and initial energy. Coupled nonlinear governing system equations are treated with the multiple scale methods with different assumptions depending on applied loads. Fast and slow system dynamics are revealed leading to detection of different possible dynamical regimes. The choice of the design parameters of the nonlinear energy sink is discussed and a tuning method is proposed. The efficiency of the control is validated by an experimental study: a physical model of the pendulum is excited by the shake table. The response of the system shows that the nonlinear energy sink is able to control the main system.