A recent active vibration absorption method, the Delayed Resonator (DR) is considered. The DR absorber is implemented on a flexible beam, and the dynamic features of this structure are studied. An analytical model of the system is developed in order to predict the experimental findings. Instead of the earlier finite difference method, modal co-ordinate representation is adopted here. In particular, the stability features obtained through analytical and experimental studies are compared. The boundary conditions (BCs), i.e., the beam's clamping structure, dictate the restoring forces on the beam-absorber system, and therefore, play an important role on the system stability. In the experimental work the results are generated under the present beam BCs. For the analytical study, however, they have to be carefully formulated. In order to reflect the physical reality some unconventional BCs are used on the beam. This forms an important part of the ''modelling'' effort presented here. The results obtained concur with the experimental findings better than the earlier dynamic models which use the finite difference method and ideal clamped-clamped BCs. In summary, modal representation with the unconventional BCs are suggested as an analytical tool for the design of DR absorbers operating on beams.