The inspiration for this project comes from atomic force microscopy. In non-contact mode, the sharp tip of an atomic force microscope oscillates near the sample surface and atomic interactions affect the amplitude of its vibration as measured by a laser beam reflected from the cantilever surface. This dependence on the amplitude of the vibration on the distance from the sample allows the sample topography to be mapped over the course of many scans with the tip. This process allows one to infer the topography of a material at a nanoscale level without ever having to touch said material. This design project employs the theory of a non-contact AFM on a macroscopic level.

 

This was done by attaching a magnet to the tip of an acrylic cantilever beam, which was then vibrated at a frequency slightly over resonance. The magnetic force between the beam and the sample altered the resonant frequency of the cantilever, providing information on how far from the sample the vibrating beam was. Through careful iterative adjustments of the distance between the sample and the cantilever, in to obtain the same resonant response along different portions of the sample, the topography of the steel surface could be inferred.

 

Before testing the final system,  detailed calculations were carried out in MATLAB in order to correctly chose a cantilever beam with desirable vibrational properties. The resonant behavior of the test system was predicted by numerically solving a noninvertible differential equation.