A semi-submersible floating platform (10, 10A) for use in offshore applications has a semi-submersible hull structure (11) including support columns (12), a pontoon structure (13) adjoined to the lower ends thereof, and a deck structure (14) supported at an upper end of the columns for supporting the deck and equipment mounted thereon above the water surface. One or more passive damper weight members (15) are suspended below the hull by flexible connection members (16) at variable distances to provide hydrodynamic mass, damping, and in-water weight to the platform during operation, and the flexible connection members are maintained in tension by the damper weight(s) during operation.