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Elasticity has been linked to the remarkable propulsive efficiency of pulse-jet animals such as the squid and jellyfish, but reports that quantify the underlying dynamics or demonstrate its application in robotic systems are rare. This work identifies the pulse-jet propulsion mode used by these animals as a coupled mass-spring-mass oscillator, enabling the design of a flexible self-propelled robot. We use this system to experimentally demonstrate that resonance greatly benefits pulse-jet swimming speed and efficiency, and the robot's optim