Motion of a Simple Pendulum: A Digital Technology Approach

Autor/inn/en	Rivera-Figueroa, Antonio; Lima-Zempoalteca, Isaías
Titel	Motion of a Simple Pendulum: A Digital Technology Approach
Quelle	In: International Journal of Mathematical Education in Science and Technology, 52 (2021) 4, S.550-564 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2019.1692934
Schlagwörter	Motion; Mathematical Models; Educational Technology; Technology Uses in Education; Mathematics Instruction; Calculus; Equations (Mathematics); Computer Software + Suchen Sie Ihr Suchwort? Bewegungsablauf; Mathematical model; Mathematisches Modell; Unterrichtsmedien; Technology enhanced learning; Technology aided learning; Technologieunterstütztes Lernen; Mathematics lessons; Mathematikunterricht; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Equations; Mathematics; Gleichungslehre
Abstract	In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed. This is due to the impossibility of expressing, in terms of simple elementary functions, the solutions of the nonlinear differential equation (NLDE) that models the pendulum, which is why the authors usually choose the linearized differential equation arising from the sin [theta] [approximately equal to] [theta] approximation for small angles [theta]. In this article, we use the computational power of "Mathematica" software and take advantage of its capacity to graphically show the solutions of the NLDE. In this manner, we determine approximations of the periods that result from varying the initial amplitude [theta][subscript 0], without assuming that it takes small values. From a comparison of the solutions of both types of modelling of a simple pendulum, a criterion for deciding how small [theta][subscript 0] must be for the linear equation to be adequate for modelling is obtained; this comparison includes an analysis of the pendulum's motion when the cable length and the gravitational acceleration constant are varied. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01