A passively damped mechanical system is disclosed, for example for use in aerospace applications where vibration can adversely affect navigational and operational instruments. In one example, the passively damped mechanical system includes an end fitting (110) of a strut (106) used to connect a structural element (102) to a payload (104). The end fitting (110) may include outer and inner cylindrical hubs (120, 122), with a space between the outer and inner cylindrical hub (120, 122) at least partially filled with a viscoelastic material (136). In a further example, the passively damped mechanical system includes legs (204) used to connect a structural element (102) to a bracket (200) configured to support a payload. Each leg (204) may include a hollow interior having a lattice (208) structure to add strength and a viscoelastic material (210) to provide passive damping.