A damping apparatus can be self-centering and include one or more pre-compressed and preloaded mechanical springs. A solar tracking apparatus can include a solar panel mounted on a rotating shaft, and a self-centering damping apparatus operatively connected to the rotating shaft to compensate for torque created when the solar panel is rotated at an angle to horizontal. A steering assembly for a zero-turn riding lawn mower can include a pair of steering levers and a self-centering damping apparatus operatively connected to the steering levers.