Taking advantage of the vastly different time scales of the problem, a simple analytical model of HOM induced relaxation oscillations has been developed. First a continuous approximation of the impulsive discrete forces is made. Then only the components of the force with the synchrotron frequency are retained to describe the slowly varying amplitude and frequency of the relaxation oscillation. A two particle version of this model reproduces the main characteristics of the system. ©1999 American Institute of Physics.