This project is engaged in a program of research which is directed at the study of the mechanism of forced vibrations in machine tool-metal cutting systems. Analytical methods, test and specification techniques have been developed that should significantly aid machine tool manufacturers in the design of essentially vibration-free machine tools for given cutting operations. The types of disturbances which cause forced vibrations in machine tools are described and categorized. The detrimental effects upon performances, which these disturbances have during cutting operations, are discussed. An attempt is made to show that the problem of forced vibrations in metal cutting systems can be generalized and simplified to a very large extent. The analytical methods to be used in this general approach are developed, and the experimental results obtained therefrom are discussed. In order to accomplish the objectives of this program the study of the mechanism of forced vibrations was divided into two main areas. The first of these areas is concerned with the effects of forced vibration due to variations in cutting depth and disturbances from internal and external forces. The remaining phase of this program is concerned with the effects of forced vibration caused by the transmission of forces through the foundation. (Author).