Free oscillations and visualization of solutions of their differential equations by experiment

using the example of the problem of free undamped oscillations of a mechanical system, the article shows how to teach a student [1] who has not studied solutions of differential equations in higher mathematics yet, to make a differential equation of such oscillations and find its solution. This possibility is based on an experiment [2], thought or organized literally by improvised means, as a result of which it is easy to establish the nature of the dependence of the variable on time, and then, if students have solid knowledge in the volume of a school mathematics course, to make a differential equation of such fluctuations. In fact, such an experiment [3] visualizes the solution of the differential equation of this problem, which facilitates the perception of the material and minimizes the dependence of the student's perception of this section of physics on the level of his knowledge of higher mathematics. Similarly, it is possible to predict the type of dependence of a variable on time for free damping vibrations of a mechanical system and obtain a differential equation describing such fluctuations. Students' understanding of the basics of the theory of mechanical vibrations in the course of general physics will help them to further assimilate the material easier when studying special courses on the theory of vibrations [4].

harmonic oscillations, differential equation, solution, physics, experiment, students