The focus of the work is the "phase lock-on", a well-known phenomenon observed in oscillating dynamical systems where the forcing and output frequencies are synchronized. This phenomenon appears to be universal with the frequencies related by a rational ratio. We considered the case of an incompressible flow past a confined cylinder where the incident bulk flow is subjected to periodic velocity perturbations. While we considered both Newtonian and non-Newtonian (Bingham) fluids, the main interest was on the Bingham case. Numerical simulations were conducted at a fixed Reynolds number of Re = 100 based on the bulk fluid velocity and cylinder diameter. The relative amplitude of the periodic velocity perturbation was considered in the range 0.10-0.30 and the forcing frequency relative to the natural unforced shedding frequency was in the range 1.4-2.3. These choices yielded fixed lock-on periodic states that correspond to the number 2 on the horizontal axis of an Arnold tongue graph. Yield stress effects are shown for Bingham numbers in the range 0-0.5.