This paper simplifies the analysis of the dynamic response of structures to a sinusoidal loading to provide arithmetic solutions and a means of understanding the dynamic response of a structure. It also provides a means to estimate the characteristics (mass, stiffness and damping) of a TMD to address any residual problematic dynamic response. This enables the design provision for the additional weight attached to the structure and the required space, if a TMD is deemed to be necessary. A worked example of a simply supported welded steel box girder footbridge is presented.