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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-23 18:01 |
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Conference: Bucharest University Faculty of Physics 2023 Meeting
Section: Physics Education
Title:
Mathcad work documents for the study of the simple gravitational pendulum
Authors:
Adriana RADU(1,3), Ionel GRIGORE(2), Valentin BARNA(3)
*
Affiliation:
1) “Mihai Viteazul” National College, Ploieşti, Romania;
2) “Ion Luca Caragiale” National College, Ploieşti, Romania;
3) Faculty of Physics, University of Bucharest, Bucharest-Măgurele, Romania
E-mail
grigore_1965@yahoo.com
Keywords:
Mathcad, didactic tool, gravitational pendulum, oscillation period, elliptic integral, physics education
Abstract:
This paper presents a didactic tool designed with Mathcad work documents for the study of the simple gravitational pendulum in oscillation mode. For a certain value of the initial angular amplitude, entered in the input data, the period of the pendulum is calculated and compared with the approximations of order zero, one and two from the expansion series. For the calculation of the period, it is shown how the full elliptic integral of the first kind can be evaluated in Mathcad with the initial angular amplitude of the pendulum as a parameter. On the same graph are superimposed the curves that reproduce the dependence of the period and the approximations of the zero, first and second order on the initial angular amplitude. The facilities of the Mathcad program can be explored to quickly calculate the values of an indexed quantity by an index. Thus, we have generated the table with the values of the oscillation period depending on the values of the initial angular amplitude. Also, on the same graph, the errors relative to the calculation of the period in the zero, one and two orders were graphically represented for comparison. By using the tool in class, students can calculate the period of the gravitational pendulum at any value of the initial angular amplitude and clarify under which conditions the movement of the pendulum can be approximated in zero, one and two orders depending on practical needs.
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