An analysis of the longitudinal forces and the resulting longitudinal motions of an idealized drill string is presented. The only external force excitation considered occurs at the bit and is due to the intermittent contact of the teeth with the bottom of the hole. Attention has been restricted to the following two salient possibilities: 1 - Excitation at the bit may develop oscillating forces at the bit with amplitudes of the same order of magnitude as those of the bit load. 2 - Appreciable bit load variation may be detected by instruments which measure the motion of the drill string near its top. The first possibility is important if maximum penetration rate is to be achieved, and the second possibility is important in implementing practical measurement of the phenomenon. From the results of the specific example considered in this report, it is concluded that possibilities 1 and 2 may occur in sufficient magnitude to be influential, but experimental data on the actual bit motion and the damping will be required to evaluate the effect. The analysis is presented in such form that the influence of the various parts of the system can easily be evaluated.
