This paper presents an Euler-Bernoulli microcantilever beam model utilized in non-contact Atomic Force Microscopy (AFM) systems. A distributed-parameters modeling is considered for such system. The motions of the microcantilever are studied in a general Cartesian coordinate with an excitation at the base such that beam end with a tip mass is subject to a general force. This general force comprising of two attractive and repulsive parts with high power terms is taken as the atomic intermolecular one which has a relation with the displacement between the tip mass and the surface such that the total general force will be in the form of an implicit nonlinear equation. It is most desired to observe the effects of the base excitation in high frequencies on the tip van der Waals interaction force. Hence, the general force will produce a peak in the FFT spectrum corresponding to the frequency of the base.