Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood's machine

American Journal of Physics

Volumn 67, Issue 3, 1999, Pages 228-235

  Pecori, Barbara ^b   Torzo, Giacomo ^a   Sconza, Andrea ^b  

^a Area Della Ric Corso Stati U   (Italy)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033413747     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19230     Document Type: Article

References (19)

1. From now on, the constants k, k′, k″, κ, κ′ . . . will be assumed to be positive.
2. 3 oscillator," Phys. Teach. 30, 249-250 (1992); N. C. Bobillo-Ares and J. Fernandez- Nunez, "Two-dimensional harmonic oscillator on air table," Eur. J. Phys. 16, 223-227 (1995).
3. 3 oscillator," Phys. Teach. 30, 249-250 (1992); N. C. Bobillo-Ares and J. Fernandez- Nunez, "Two-dimensional harmonic oscillator on air table," Eur. J. Phys. 16, 223-227 (1995).
4. 3 oscillator," Phys. Teach. 30, 249-250 (1992); N. C. Bobillo-Ares and J. Fernandez- Nunez, "Two-dimensional harmonic oscillator on air table," Eur. J. Phys. 16, 223-227 (1995).
5. 3 oscillator," Phys. Teach. 30, 249-250 (1992); N. C. Bobillo-Ares and J. Fernandez-Nunez, "Two-dimensional harmonic oscillator on air table," Eur. J. Phys. 16, 223-227 (1995).
6. 2 should be taken into account: this, however, requires the calculation of the geometrical factor k that depends on the body shape.
7. A detailed analysis of this kind of motion was made by I. R. Gatland, "Theory of a nonharmonic oscillator," Am. J. Phys. 59, 155-158 (1991).
8. nΧ," Phys. Teach. 34, 196 (1996)], where he claims that a single cone would produce a purely cubic restoring force.
9. The data and graphics reported in this paper were taken with an interface (model ULI-II) produced by Vernier Software (Portland, OR), but similar performances were obtained using an equivalent interface (model 500) produced by PASCO (Roseville, CA).
10. The "Rotary motion sensor" is available both from Vernier Software and PASCO. A similar device can be home built using one of the encoders contained in the "mouse" that comes with any PC, as explained by O. Ocho and N. F. Kolp, "The computer mouse as data acquisition interface," Am. J. Phys. 65, 1115-1118 (1997).
11. We used an electronic balance with an accuracy of 0.1 g to measure the weight of ten equal metal washers for a total of 11.2 g. Each time one extra mass m is displaced from one body to the other, the force changes by the quantity F = 2mg = 0.0224 N.
12. The cylinder top and bottom have spherical shape in order to reduce the oscillation damping.
13. This "mass trimming" is obtained by using small lead spheres (those normally used to load fishing wires) that were clamped to the wire above the counterweight.
14. h/script M sign) of about 2%.
15. This effect can also be detected by a careful inspection of the plot of Fig. 8. The full circles belong alternately to straight lines with different slopes: those marked "OUT" are the period values calculated from half-periods spent "out of water" (an expected smaller slope) while those marked "IN" are calculated from half-periods "inside water" (an expected larger slope).
16. This can also be detected by a careful eye inspection because the free water surface moves up and down by about 1.3 mm.
17. V. F. Weisskopf and H. Bernstein, "Search for simplicity: Thermal expansion," Am. J. Phys. 53, 1140-1141 (1985).
18. nΧ harmonic motion," Phys. Teach. 33, 562-564 (1995).
19. Available for Macintosh and PC-IBM from Wolfram Research (at low cost in the Education version for teachers and students).