A Note on the Two-Spring Tomlinson Model

In this note, quasistatic solutions of a two-mass-two-spring Tomlinson model for atomic force microscopy are derived, and are compared with the corresponding results of the single-spring Tomlinson model. It is clarified that the solutions of the two models are equivalent provided that the effective spring constant is correctly defined. It is also shown that modeling the onset of stick-slip motion in terms of the criteria defined by explicit tip and cantilever stiffness is the most convenient to investigate the effects of the tip-flexibility on the stick-slip motion.