Educación

A model of oscillator with variable mass

 

H. Rodrigues^a*, N. Panza^a, D. Portes Jr^a, A. Soares^b

 

^a Departamento de Física, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Av. Maracaná, 229, 20271-110, Rio de Janeiro, RJ, Brazil, * e-mail: harg.astrophys@gmail.com

^b Departamento de Matemática, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Av. Maracanã, 229, 20271-110, Rio de Janeiro, RJ, Brazil.

 

Received 8 April 2014
accepted 12 May 2014

 

Abstract

We discuss the general form of Newton's second law for variable mass systems. We then derive the equation of motion of one-dimensional oscillator with time-varying mass. The obtained equation of motion is then analytically solved and the solutions are represented by means of Hypergeometric functions. The work is addressed to physics class at undergraduate level.

Keywords: Newton's second law; variable mass systems; oscillators; hypergeometric functions.

 

PACS: 45.20.D-;02.30.Hq

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Bibliografía

1. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. 1 (Addison-Wesley 1964).         [ Links ]

2. M. S. Tiersten, Am. J. Phys. 37 (1969) 82.         [ Links ]

3. K. R Symon. Mechanics 3rd edn, (Addison-Wesley 1971).         [ Links ]

4. M. Alonso and E. J. Finn, Physics Vol. 1, (New York: Academic 1992).         [ Links ]

5. I. Campos, J. L. Jiménez, and G. del Valle, Eur. J. Phys. 24 (2003) 469.         [ Links ]

6. A. R Plastino. and J. C. Muzzio, Celestial Mechanics and Dynamical Astronomy 53 (1992) 227.         [ Links ]

7. H. Irschik and H. J. Holl, Appl. Mech. Rev. 57 (2004) 145.         [ Links ]

8. H. Rodrigues, M. O. Pinho, D. Portes Jr, and A. J. Santiago, International Journal of Mathematical Education in Science and Technology 40 (2009) 523.         [ Links ]

9. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, New York: Dover (1972).         [ Links ]

10. G. E. Andrews, R. Askey, and R. Roy, Special Functions, (Cambridge: Cambridge University Press 1999).         [ Links ]