This paper describes a time-evolving digital twin and its application to a proof-of-concept engineering dynamics example. In this work, the digital twin is constructed by combining physics-based and data-based models of the physical twin, using a weighting technique. The resulting model combination enables the temporal evolution of the digital twin to be optimised based on the data recorded from the physical twin. This is achieved by creating digital twin output functions that are optimally-weighted combinations of physics- and/or data-based model components that can be updated over time to reflect the behaviour of the physical twin as accurately as possible. The engineering dynamics example is a system consisting of two cascading tanks driven by a pump. The data received by the digital twin is segmented so that the process can be carried out over relatively short time-scales. The weightings are computed based on error and robustness criteria. It is also shown how the error and robustness weights can be used to make a combined weighting. The results show how the time-varying water level in the tanks can be captured with the digital twin output functions, and a comparison is made with three different weighting choice criteria.