A shaft and bearing system was developed with natural frequencies in the range of 8,000 to 60,000 rpm for the purpose of determining the practicality of low-speed harmonic excitation of high-speed natural frequencies. The analytical development and analysis utilized SPAR, a finite element program, and a bearing stiffness program to determine frequencies for the first through fourth harmonics of natural frequencies under 60,000 rpm. A misaligned flexible disc coupling was used to input a forcing function with a frequency of N times the running speed and thereby excite the natural frequencies in the Nth harmonic at the running speed. Most of the analytical results had corresponding experimental results; however, many increased vibration levels did not correlate with analytical results. Four frequency response plots are presented. A comparison of these plots and analytical results are presented in the form of a Campbell diagram. Although the experimental results are not supportive enough to be conclusive, they do indicate that low-speed harmonic excitation may be a method of predicting high-speed natural frequencies. Major difficulties were encountered in the experimental program which are described, and some alternative investigations are proposed. / M.S.