A shock-absorbing platform includes a bottom plate and a top plate joined to one another along at least two sides by elongate rigid links that enable the plates to remain in parallel relation to one another as the plates are displaced responsive to externally-imparted forces. An air spring resists relative vertical motion between the bottom and top plates as external forces are applied to the platform. A shock-absorbing damper damps the natural oscillation of the air spring. The resistance presented by the air spring is adjustable through an inlet and outlet port in fluid communication with a remote source of air under pressure. In a second embodiment, a seat bottom includes arched leaf springs that supplant the air spring to increase the range of relative movement between the top and bottom plates and to lower the profile of the seat bottom.