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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 2:04 |
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Conference: Bucharest University Faculty of Physics 2012 Meeting
Section: Educational Physics
Title:
Tools for NASA`s Methods in Schools - Numerical and Analytical Study of the Mechanical Oscillations
Authors:
I. GRIGORE(1), T. FERENER-VARI(2), H.V. TOMA(2), I. OPRESCU(2)
Affiliation:
(1)"Lazar Edeleanu" National College, Ploiesti, Romania
(2)"Mihai Viteazul" National College, Ploiesti, Romania
E-mail
grigore_nl@yahoo.com
tonio_fv07@yahoo.com
Horia_TOMA_CD@yahoo.com
oprescu65@yahoo.com
Keywords:
numerical analytical study mechanical oscillations
Abstract:
Our spread sheets are useful to achieve primarily didactic goals and also to produce the pleasure of learning by a comparative study of two solutions of the same differential equation. That equation is obtained by applying Newton`s second law of motion. The numerical solution is important because the problem of three (or more) bodies has not an analytical (closed form) solution. NASA experts can use computerized algorithms for approximation. We have created special spreadsheets which show the numerical solution. One of our sheets shows three thousands of lines with numbers. They are the results obtained for three second of damped oscillations. Each line corresponds to a millisecond and shows the initial and the final coordinates y and y-velocity, the constant net force, the acceleration, the change in y-velocity, the average velocity and the change in y. The values of a line show the way in which the computer find a solution for the fundamental problem of dynamics (by applying the knowledge which the students can obtain in high school). The initial values of y and y-velocity of the first interval of time are given. The initial values of any other interval of time are equal to the precedent final values. The forces which depend on y and y-velocity are calculated by using the initial values. We have created didactic software - in academical style - thinking to NASA software and computer games necessary to find the moment and the place to start the action of a rocket engine and the duration of that action. One of our didactic computer games can be used to find the moment and the place in which the potential energy is equal to the kinetic energy. The other one can be named: Increase the damping ratio to find the condition for critical damping.
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