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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-23 18:30 |
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Conference: Bucharest University Faculty of Physics 2022 Meeting
Section: Physics Education
Title:
An Excel didactic tool to simulate the composition of the perpendicular harmonic oscillations
Authors:
Adriana RADU (1,2), Ionel GRIGORE (3), Valentin BARNA (1)
*
Affiliation:
1) Faculty of Physics, University of Bucharest, Bucharest-Măgurele, Romania
2) “Mihai Viteazul” National College, Ploieşti, Romania
3) “Ion Luca Caragiale” National College, Ploieşti, Romania
E-mail
fizica.prahova@gmail.com; grigore_1965@yahoo.com; barnavalentin@yahoo.com
Keywords:
Excel, didactic tool, harmonic oscillations, Lissajoux figures, Physics Education
Abstract:
The present paper describes an interactive didactic tool created with the help of Excel spreadsheets to simulate the composition of the perpendicular harmonic oscillations. The periods and amplitudes of the oscillations are used as input data, together with the phase difference between them. The graph placed next to the input data renders the resultant trajectory obtained by the composition of the two oscillations. Depending on the ratio of the frequencies and the phase difference the Lissajoux figures are obtained. It is thus verified that when the ratio of the oscillation frequencies is a rational number stable closed trajectories are obtained, while when the ratio of the frequencies is an irrational number the trajectories are open and they gradually cover an area. In addition, the particular case when the frequencies of the oscillations are equal is verified, and thus an elliptic resultant trajectory is obtained. The position of the mass point on the resultant trajectory can be visualized at any moment of time introduced in the input data. The Cartesian coordinates and the polar coordinates of the mass point are calculated. Concurrently, in the time moment set in the input data, the velocity of the mass point are calculated. Besides the main graph with the resultant oscillation, there are placed, on the same spreadsheet, two more graphs showing how the velocity depends on the Cartesian coordinates. By creating and using this tool in the classroom, students can study in an interactive and pleasant manner, how two perpendicular harmonic oscillations are composed. The rapid feedback for the input data change allows, in a short timeframe, the analysis of a large number of Lissajoux figures. Thus, students are able to assimilate more easily the knowledge regarding the composition of perpendicular harmonic oscillations.
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