UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2022-07-01 15:59

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Conference: Bucharest University Faculty of Physics 2019 Meeting


Section: Physics Education


Title:
Uni and bidimensional tautochrone movements


Authors:
Catalin BERLIC(1), Manuela DRENEA(2), Cristina MIRON(1), Emil-Stefan BARNA(1)


Affiliation:
1) Faculty of Physics, University of Bucharest, Bucharest-Magurele, Romania

2) “Radu Negru” National College, Fagaras, Romania



E-mail
cberlic@gmail.com, barnavalentin@yahoo.com


Keywords:
Tautochrone movements, cycloidal pendulum, physics education.


Abstract:
Many problems in the study of physics have to do with boundary/extremum situations. The basic approach is analogous with that of finding the extremum of a function in ordinary calculus. Historically and pedagogically, the prototype problem introducing the calculus of variations is the “brachistochrone” (from the Greek for “shortest time”). The cycloid curve is the solution to the brachistochrone problem (the curve between two points along which a body can move under gravity in a shorter time than for any other curve) and for the tautochrone / isochrone situation (the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point). We take into account the elastic pendulum case by including the geometrical and mass properties; we propose a dynamical model for the study of the tautochrone movement. We consider also the situation of the cycloidal pendulum.