High vibration associated with equipment used in the mining, extraction, and processing of mineral resources degrades structural components, often leading to catastrophic failure and loss of productivity, and excessive noise can result in permanent hearing loss. To foster efficient utilization of the nation's mineral resources and minimize mineral processing occupational hazards, the Bureau of Mines investigated the relationship between the microstructures of carbon and alloy steels and cast irons and their damping capacities (ability to absorb vibration). Researchers measured damping capacity and other properties and investigated the effects of carburizing, spheroidizing, and annealing. In carbon and alloy steels, rounded colonies of fine-grained pearlite in a ferrite matrix correlate well with low damping capacity. Steel microstructures of sharp-faceted pearlite in ferrite matrix and spheroidized cementite in ferrite show higher damping. In cast irons, the lowest damping capacity is associated with nodular graphite microstructure, and the specific damping capacity (SDC) increases as the microstructure progresses from nodular to compacted to flake. Predominant ferrite in cast irons is also associated with good damping. SDC data are presented for selected carbon and alloy steels and cast irons.