On the dynamics of a harmonic oscillator undergoing impacts with a vibrating platform

This paper deals with a model for repeated impacts of a mass attached to a spring with a massive, sinusoidally vibrating table. This model has been studied in an attempt to understand the cantilever-sample dynamics in atomic force microscopy. In this work, we have shown that for some values of the frequency of the vibrating table, there are countably many orbits of arbitrarily long periods and the system is sensitive to the initial conditions with which the experiments are conducted. We have also shown existence of complex dynamics in the cases when the natural frequency of the spring-mass system is very low; and when it is the same as the oscillating frequency of the table.