In the study of floating structures under the influence of realistic environmental conditions, we have obtained theoretical results of interest for the analysis of anomalous waves. In this work, we present relevant analytical results to study specific short-time waves, both as an isolated event and as a part of a complex long event measured from experiments. This is possible because wave dynamics data acquired by the National Data Buoy System of NOAA are processed via a short-time Fourier Transform. When such data are incorporated in our theoretical results, closed-form expressions of dynamic mooring line displacement and tension are computed, both in frequency and time domain. Our theoretical tools for the analysis of anomalous waves rely on a linearized model of a mooring line, under the assumption of small values of mooring length compared to the characteristic length of elastic longitudinal waves. We show a proof of concept of these tools, by the comparison of three ocean wave events. These results provide a preliminary framework for qualitative analysis of waves acting on mooring systems with minimal computational cost.