Finite amplitude, horizontal motion of a load symmetrically supported between isotropic hyperelastic springs

► Two exact integrals for the finite motion of a load supported by hyperelastic springs are derived. ► Inertia of the springs is included, and a general relation for the small amplitude frequency follows. ► Periodicity for arbitrary finite motions is proved for all hyperelastic springs with monotone engineering stress. ► The exact closed form finite amplitude solution is obtained for the neo-Hookean material. ► The period is given by the Heuman lambda function, and the overall system behavior is discussed.