  Flagella and cilia are examples of actively oscillating, whiplike biological
filaments that are crucial to processes as diverse as locomotion, mucus
clearance, embryogenesis and cell motility. Elastic driven rod-like filaments
subjected to compressive follower forces provide a way to mimic oscillatory
beating in synthetic settings. In the continuum limit, this spatiotemporal
response is an emergent phenomenon resulting from the interplay between the
structural elastic instability of the slender rods subjected to the
non-conservative follower forces, geometric constraints that control the onset
of this instability, and viscous dissipation due to fluid drag by ambient
media. In this paper, we use an elastic rod model to characterize beating
frequencies, the critical follower forces and the non-linear rod shapes, for
prestressed, clamped rods subject to two types of fluid drag forces, namely,
linear Stokes drag and non-linear Morrison drag. We find that the critical
follower force depends strongly on the initial slack and weakly on the nature
of the drag force. The emergent frequencies however, depend strongly on both
the extent of pre-stress as well as the nature of the fluid drag.
