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Instabilities can generate fast and amplified motion in mechanical systems. Here, we present an elasto-magnetic instability that combines magnetic attraction and elastic tension to create bistable dynamics. To demonstrate this, we built a coupled elasto-magnetic vibration system that produces amplified motion and greater displacement and force than a control system across a wide frequency range. We also establish design principles that can be applied to different configurations by studying the balance between magnetic and elastic forces. The system also shows inertial hysteresis, which enables mechanical memory by storing external inputs in volatile and non-volatile modes with adjustable thresholds. This dual function of amplification and memory shows how instabilities can be potentially used for programmable and adaptive soft actuation.