An offshore system for petroleum production has a buoyant platform. A tendon assembly secures to the platform and extends down to a counterweight located near the lower end. A piling is embedded in the sea floor. A socket at the counterweight telescopingly slides over the upper end of the piling to prevent lateral movement of the platform. A dampening chamber is located between the socket and the piling. Ports for the chamber are arranged to allow a faster downward movement of the piling than upward movement.