RELATIONSHIP BETWEEN PHYSICAL AND MATHEMATICAL ASPECTS DURING STUDYING THE TOPIC “OSCILLATIONS” AT A TECHNICAL UNIVERSITY
The article, mainly, is dedicated to the discussion of a relation between physical and mathematical aspects of teaching the free, damping, and induced oscillations in technical university to the rising bachelors of engineering and technology. Firs of all, we propose to teach this topic using the notions of the generalized coordinate, generalized momentum, generalized mass, and generalized stiffness. This allows to unify the studying of physically different types of oscillation (mechanical, electrical, etc.). Second, we emphasize that mathematically these oscillating processes are described by linear differential equations (often non-homogeneous ones) which might be solved by an effective algorithm presented in several mathematical textbooks (this algorithm sometimes is called as the Lagrange method, sometimes it is mentioned as the Duhamel principle). We demonstrate that, in standard general physics textbooks, during the presentation of the topic “Oscillations”, this algorithm is not addressed. As a result, as it usually happens in universities, a gap appears between the physics and mathematics which reduces the efficiency of both subjects studying. While teaching the mathematics in a technical university, it is important to demonstrate for which physical problem the studying material might be applied. In the article, a new approach for teaching the topic “Oscillations” is proposed; it includes the indicated effective mathematical algorithm (the Lagrange method)