Theory of Harmonic Oscillations: A Gross Error in Physics

Abstract

The critical analysis of the foundations of the standard theory of harmonic oscillationsis proposed. The unity of formal logic and rational dialectics is methodological basis ofthe analysis. The analysis leads to the conclusion that this theory represents gross error.The substantiation (validation) of this statement is the following main results. I. In thecase of the material point suspended on the elastic spring, the linear differentialequation of harmonic oscillations is the equation (condition) of balance of Newton’sforce (Newton’s second law) and “Hooke’s force” (“Hooke’s law” as pseudolaw). Thisequation contains the following gross methodological errors: (a) the differentialequation of motion of the material point does not satisfy the dialectical principle of theunity of the qualitative and quantitative determinacy of physical quantities (i.e.,Newton’s force and Hooke’s force). In other words, the left and right sides of thedifferential equation (i.e., the equation of balance of the forces) have no identicalqualitative determinacy: the left side of the the equation of balance of the forcesrepresents Newton’s force, and the right side of the the equation of balance of the forcesrepresents the “Hooke’s force” (as pseudolaw); (b) the sum of Newton’s force and the“Hooke force” (as pseudolaw) in the the equation of balance of the forces is equal tozero. This means that the sum of the numerical values of Newton’s force and “Hooke’sforce” (as pseudolaw) is equal to zero. Consequently, the numerical values of Newton’sforce and “Hooke’s force” (as pseudolaw) are equal to zero in the region of neutral realnumbers. This means that the equation of balance of the forces is incorrect; (c) “Hooke’sforce” (as pseudolaw) in the equation of balance of the forces represents the product ofthe spring constant (coefficient of stiffness of the spring) and the coordinate of thematerial point. In this case, “Hooke’s force” (as pseudolaw) does not represent Hooke’slaw. “Hooke’s force” (as pseudolaw) contradicts to Hooke’s law because the coordinateof rhe material point does not determine the spring constant (coefficient of stiffness ofthe spring).