Elastically suspending a load with a compliant suspension system can increase the energy efficiency of legged locomotion and load carrying in humans, animals, and robots. In prior work, we developed a simple linear model from first principles and showed that elastically-suspended loads reduce the energy cost and stability of locomotion. In this paper, we expand on this model by adding flight phases, transforming it into a nonlinear hybrid system that is a more realistic representation of human hopping and high-speed locomotion more generally. The addition of flight phases causes a counterintuitive shift in the behavior of the double-mass coupled-oscillator system. With the addition of flight phases, the tuning of the elastic load suspension becomes more critical in order to reduce the energy cost of human hopping. Elastically-suspended loads also increased the overall system stability compared to rigidly-attached loads when the system exhibits flight phases. Therefore, under certain conditions, a human hopping with an elastically-suspended load can exhibit increased energy efficiency and stability compared to a rigidly-attached load. This study will help improve our understanding of elastically-suspended loads and could enable the design of tuned suspension systems for load carrying.

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