Energy and damping in an SDOF system subjected to a variable forcing frequency

In order to model the dissipative effect due to variable forcing frequency, the authors presented in a previous article an original method based on an additional dimension and on the relativity concept. The associated metric of the space was identified experimentally, and the equation of motion was obtained from geodesic equations. In the present article the equation of motion is formulated by using the Newtonian approach. The total kinetic energy obtained has an original general expression that is reduced either to Einsteinʹs energy in the presence of no variable forcing frequency, or to the classical expression in the case of no relativist effects, and which validates the assumptions made on the metric. An experiment carried out on a single-degree-of-freedom system is used to validate the approach.