Differential Equations Applied to Atomic Force Microscopy: A Strategy to Classical Mechanics Teaching in Undergraduation
Gerson A. C. Lopes *
Education Center in Science, Engineering and Mathematics, State University of Amapá, Av. Presidente Vargas, 650, Campus I, 68900-070, Macapá, Amapá, Brazil.
Eduardo A. Cotta
Department of Physics, Laboratory of Materials Optics, Federal University of Amazonas, Av. General Octávio, Coroado I, Manaus, Amazonas, Brazil and National Institute of Science and Technology of Semiconductor Nanomaterials, INCT-DISSE, Semiconductor Laboratory – CETUC/PUC-Rio, Rua Marquês de São Vicente, Rio de Janeiro, Brazil.
Henrique D. da Fonseca Filho
Materials Science Laboratory, Federal University of Amapá, Rod JK Km 2, 68902-280, Macapá, Amapá, Brazil.
*Author to whom correspondence should be addressed.
Abstract
Aims: To purpose a didactic mechanism for the teaching of the physical and mathematical concepts with respect to the mechanical oscillations, which is commonly addressed in undergraduate courses in Physics, in the chair of Classical Mechanics or correlated ones.
Place and Duration of Study: The study was performed in the Physics Department of Federal University of Amapá, Macapá-AP, Brazil during the year of 2015.
Study Design: In order to give an application of the content “mechanical oscillations” we first introduce the theory of Atomic Force Microscope. Then we get the equation of motion for the AFM cantilever, which models a non-linear driven harmonic oscillator with damping, and solve it considering different physical situations.
Methodology: We emphasize the methods of resolution of differential equations, attempting to relate its applications in condensed matter physics, in particular to atomic force microscopy (AFM).
Results: Throughout the motion equation for the AFM cantilever, we studied the solution of the equations for the cases of mechanical equilibrium, simple oscillations, damped oscillations, forced oscillations and damped and forced oscillations.
Conclusions: By applying the differential equations to a recent and instigating research area, the subject becomes better understood by students, gaining great results of learning. This purpose, however, need further work to confirm its educational potential by applying to an undergraduation class.
Keywords: Mechanical oscillations, atomic force microscopy, solution methods of ODE’s, physics teaching.