We describe an experiment involving a mass oscillating in a viscous fluid. The mechanical oscillator is tracked using a simple webcam, and an image processing algorithm records the position of the geometrical center as a function of time. Interesting information can be extracted from the displacement-time graphs, in particular, for the underdamped case. For example, we use these oscillations to determine the viscosity of the fluid. Our mean value of for distilled water is in good agreement with the accepted value at . The experiment has been successfully employed in an introductory laboratory setting.
REFERENCES
1.
M. S.
Longair
, Theoretical Concepts in Physics
, 2nd ed. (Cambridge U. P.
, Cambridge
, 2006
), pp. 183
–190
.2.
P.
Nakroshis
, M.
Amoroso
, J.
Legere
, and C.
Smith
, “Measuring Boltzmann’s constant using video microscopy of Brownian motion
,” Am. J. Phys.
71
, 568
–573
(2003
).3.
D.
Jia
, J.
Hamilton
, L. M.
Zaman
, and A.
Goonewardene
, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres
,” Am. J. Phys.
75
, 111
–115
(2007
).4.
R.
Newburgh
, J.
Peidle
, and W.
Rueckner
, “Einstein, Perrin, and the reality of atoms: 1905 revisited
,” Am. J. Phys.
74
, 478
–481
(2006
).5.
J. E.
Gilson
and O. A.
Boedtker
, “A damped harmonic motion experiment for use in undergraduate general physics laboratories
,” Am. J. Phys.
37
, 1157
–1158
(1969
).6.
M. F.
McInerney
, “Computer-aided experiments with the damped harmonic oscillator
,” Am. J. Phys.
53
, 991
–996
(1985
).7.
M.
Allen
and E. J.
Saxl
, “The period of damped simple harmonic motion
,” Am. J. Phys.
40
, 942
–944
(1972
).8.
V. K.
Gupta
, G.
Shanker
, and N. K.
Sharma
, “Experiment on fluid drag and viscosity with an oscillating sphere
,” Am. J. Phys.
54
, 619
–622
(1986
).9.
P.
Alexander
and E.
Indelicato
, “A semiempirical approach to a viscously damped oscillating sphere
,” Eur. J. Phys.
26
, 1
–10
(2005
).10.
P. L.
Chung
, “A linear oscillatory viscometer
,” Rev. Sci. Instrum.
44
, 1669
–1670
(1973
).11.
B.
Pecori
, G.
Torzo
, and A.
Sconza
, “Harmonic and anharmonic oscillations investigated by using a microcomputer-based Atwood’s machine
,” Am. J. Phys.
67
, 228
–235
(1999
).12.
S.
Nedev
and V. C.
Ivanova
, “Web camera as a measuring tool in the undergraduate physics laboratory
,” Eur. J. Phys.
27
, 1213
–1219
(2006
).13.
S.
Gil
, H. D.
Reisin
, and E. E.
Rodriguez
, “Using a digital camera as a measuring device
,” Am. J. Phys.
74
, 768
–775
(2006
).14.
A. P.
French
, Vibrations and Waves
, 3rd ed. (W. W. Norton
, New York
, 1971
), pp. 62
–64
.15.
L. D.
Landau
and E. M.
Lifshitz
, Fluid Mechanics
, 2nd ed. (Pergamon
, New York
, 1987
), pp. 83
–89
.16.
A. M.
Leshansky
and J. F.
Brady
, “Force on a sphere via the generalized reciprocal theorem
,” Phys. Fluids
16
, 843
–844
(2004
).17.
S. T.
Chen
and S. C.
Wang
, “Experimental determination among available theories describing the drag force exerting on steel spheres and Cu and Al cylinders moving in a viscous fluid
,” Phys. Scr.
70
, 349
–353
(2004
).18.
See, for example ⟨mathworks.com/applications/imageprocessing⟩.
19.
I. G.
Main
, Vibrations and Waves in Physics
, 3rd ed. (Cambridge U. P.
, Cambridge
, 1992
), pp. 34
–41
.20.
C.
Wohlfarth
, in Viscosity of Pure Organic Liquids and Binary Liquid Mixtures
, edited by M. D.
Lechner
(Springer
, Berlin
, 2008
), pp. 110
–120
.21.
H. W.
Xiang
, A.
Laesecke
, and M. L.
Huber
, “A new reference correlation for the viscosity of methanol
,” J. Phys. Chem. Ref. Data
35
, 1597
–1620
(2006
).22.
See, for example ⟨mathworks.com/access/helpdesk/help/toolbox/imaq/getdata.html⟩.
23.
W. B.
Case
, “The pumping of a swing from the standing position
,” Am. J. Phys.
64
, 215
–220
(1996
).24.
A. O.
Belyakov
, A. P.
Seyranian
, and A.
Luongo
, “Dynamics of the pendulum with periodically varying length
,” Physica D
238
, 1589
–1597
(2009
).25.
T. E.
Cayton
, “The laboratory spring-mass oscillator: An example of parametric instability
,” Am. J. Phys.
45
, 723
–732
(1977
).© 2010 American Association of Physics Teachers.
2010
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