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Biological springs can be used in nature for energy conservation and ultra-fast motion. The loading and unloading rates of elastic materials can play an important role in determining how the properties of these springs affect movements. We investigate the mechanical energy efficiency of biological springs (American bullfrog plantaris tendons and guinea fowl lateral gastrocnemius tendons) and synthetic elastomers. We measure these materials under symmetric rates (equal loading and unloading durations) and asymmetric rates (unequal loading and unloading durations) using novel dynamic mechanical analysis measurements. We find that mechanical efficiency is highest at symmetric rates and significantly decreases with a larger degree of asymmetry. A generalized one-dimensional Maxwell model with no fitting parameters captures the experimental results based on the independently characterized linear viscoelastic properties of the materials. The model further shows that a broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry on efficiency. Overall, our study provides valuable insights into the interplay between material properties and unloading dynamics in both biological and synthetic elastic systems. 

Efforts to transform educational systems advocate for shifting and expanding the voices of those who generate research. This study was part of a project that brought together mathematics teachers, youth workers, and researchers to create equity-centered noticing frameworks for mathematics instruction. We explore youth workers’ understandings of the relationship between local educational equity problems and larger structural forces. By applying the framework of critical bifocality, we explore how youth workers demonstrate praxis where their pedagogical responses are animated by an under- standing of the inherent linkages between broad social, economic, and political forces and educational equity issues in the local community.