Biped locomotion is complex to analyze in general. Most of the models in the literature for biped locomotion utilize hybrid dynamics. This makes the kinematics of the model simple to understand. However, it makes the model difficult to analyze in the presence of discontinuous terms in its differential equations. This article presents a continuous-time mathematical model for biped robots, modeling the discontinuities in impact with a nonlinear function. Natural oscillation is defined as a free response under damping compensation to achieve persistent oscillation. The phenomenon of natural oscillation was previously exploited in the linear dynamics of multi-segmental locomotor, and it is now extended to this continuous-time biped locomotion model with the contact force from the ground modeled as a nonlinear bump function. The idea of natural oscillation is preceded in this article by a complete framework on analysis and entrainment control. The research would ensure that these natural oscillations are responsible for forward locomotion of biped robots under certain conditions. The locomotion profile of the bipeds further validates the model that the velocity achieved through the natural oscillation is comparable to human jogging speeds when practical constraints are enforced.