Soft robots promise rich behaviors with minimal hardware by embedding part of the control in the body. We pursue this idea using flexible mechanical metamaterials as a soft embodiment and focus on the design and validation of a dynamic metamaterial platform for underactuated motion generation. We adopt a dynamic model with ligament-level viscous damping, identify its parameters from quasi-static tests, and validate it quantitatively against dynamic experiments. We compare three fabrication routes for the compliant ligaments. We then adopt an inverse-design framework that tunes the geometry so that a single sinusoidal base input produces closed-loop motion at a user-selected target region. Using a hybrid global–local optimization strategy (CMA-ES + MMA) with an angular momentum objective, the framework automatically discovers non-trivial geometries that generate clockwise or counter-clockwise limit cycles from the same reciprocal input. We further demonstrate frequency-based multifunctionality in simulation: a single architecture switches between opposing closed-loop behaviors (CW vs. CCW) when driven at distinct frequencies. Overall, the results position dynamic metamaterials as a viable soft embodiment that shifts complexity from electronics to morphology, a step toward single-actuator, multigait soft robotic matter.