<p>This research examines the impact of a continuous bias force on the behaviour of a spherical particle that is periodically compelled to move at a constant speed at infinity in a Newtonian liquid at low Reynolds numbers. The dynamics of particle motion are shown on the two-dimensional phase plane, including parameters such as the external periodic force, particle Reynolds number, constant bias force, and constant velocity at infinity. It is found that there is a range of values of the undisturbed far field motion and the constant bias where the effects of both neutralize. In this region the fluid behaves as quiescent. It is shown that the numerical simulation yields the case results with zero constant force and velocity at infinity. A Stokes’ iterative solution is also provided in this article and it is seen that the solutions are largely manifested by the periodic motion. The Reynolds number effects are dominated when it is larger than the amplitude of the periodic motion and smaller than the Strouhal number. A drifting, pulling, pushing of the particle happens due to Reynolds number, constant bias and far field velocity effects respectively. Simulations are validated by the earlier literatures and hence this simulation can be considered as a test case for simulations of more complex flows.</p>