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The focus of this work is to dissect the physical mechanisms that drive and sustain flow-induced, transverse vibrations of cylinders. The influence of different mechanisms is quantified by using a method to partition the fluid dynamic force on the cylinder into distinct, physically relevant components. In conjunction with this force partitioning, calculations of the energy extracted by the oscillating body from the flow are used to make a direct connection between the phenomena responsible for force generation and their effect on driving flow-induced oscillations. These tools are demonstrated in a study of the effect of cylinder shape on flow-induced vibrations. Relatively small increases in cylinder aspect-ratio are found to have a significant influence on the amplitude of oscillation, resulting in a large drop in oscillation amplitude at reduced velocities that correspond to the upper range of the synchronization regime. By mapping out the energy transfer between the fluid and structure as a function of aspect-ratio, we identify the existence of a low-amplitude stationary state as the cause of the drop in amplitude. Partitioning the fluid dynamic forces on cylinders of varying aspect-ratio then allows us to uncover the physical mechanisms behind the appearance of the underlying bifurcation. The analysis also suggests that while vortex shedding in the wake is necessary to initiate oscillations, it is the vorticity associated with the boundary layer over the cylinder that is responsible for the sustenance of flow-induced vibrations.