# Article

**Summary:**

The pendulum damper modelled as a two degree of freedom strongly non-linear
auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are
analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the paper [2] is performed. Both approaches are compared and conclusions are drawn.