An application of energy principles to a mechanical system

This note examines the properties of two independent energy principles: conservation of energy and the total potential energy theorem. Using a thermodynamic framework to examine a mass–spring–dashpot system, it sets out to investigate the need for the force to be applied infinitesimally slowly for the first principle to be applicable, the requirement for constant force when using the second principle, and what happens when the force is applied in an arbitrary manner. It is shown when including viscous damping and considering equilibrium states that conservation of energy principle is consistent with the external work equalling the internal work under a very slow loading rate, whereas for the total potential energy theorem the total work done is split evenly between the internal work and energy dissipated.