The inverted pendulum under different perspectives

Abstract Three different explanations for the phenomenon of inverted oscillation of a pendulum with vertically forced pivot are presented. Two of these approaches are present in the literature and a compilation of results have been presented, while a third one aims to stimulate students to associate mathematical tools with the description of the observed physical phenomenon, searching for a quantification, even approximated. The possibility of separating into different time scales of a single phenomenon feasible in the classroom becomes very clear, and the utility and limitations of this type of description are exposed. At the end of the presentation of the different explanations some numerical results are compared with the third approach, bringing the current reality of scientific research: computational simulations. It is an unparalleled opportunity for students to come in contact with diverse mathematical tools with physical intuition guiding their applications.