The motion of a Slinky walking down a set of stairs is modeled by a simple dynamical system with two degrees of freedom undergoing inelastic collisions. Numerical integration of the model’s equations of motion shows that the model’s behavior is similar to observations of the motion of an actual Slinky. In particular, it is found that the model’s motion exhibits a periodic gait, although subject to more restrictive launch conditions than an actual Slinky.
REFERENCES
1.
T. W.
Edwards
and R. A.
Hultsch
, “Mass distributions and frequencies of a vertical spring
,” Am. J. Phys.
40
, 445
–449
(1972
).2.
J. M.
Bowen
, “Slinky oscillations and the notion of effective mass
,” Am. J. Phys.
50
, 1145
–1148
(1982
).3.
S. Y.
Mak
, “The static effectiveness mass of Slinky
,” Am. J. Phys.
55
, 994
–997
(1987
).4.
M.
Sawicki
, “Static elongation of a suspended Slinky
,” Phys. Teach.
40
, 276
–278
(2002
).5.
L. M.
Reynolds
, “Folding slinky wave demonstrator
,” Phys. Teach.
16
, 652
–654
(1978
).6.
J.
Blake
and L. N.
Smith
, “The Slinky as a model for transverse waves in a tenuous plasma
,” Am. J. Phys.
47
, 807
–808
(1979
).7.
F. S.
Crawford
, “Slinky whistlers
,” Am. J. Phys.
55
, 130
–134
(1987
).8.
G.
Vandegrift
, T.
Baker
, J.
DiGrazio
, A.
Dohne
, A.
Flori
, R.
Loomis
, C.
Steel
, and D.
Velat
, “Wave cutoff on a suspended slinky
,” Am. J. Phys.
57
, 949
–951
(1989
).9.
F. S.
Crawford
, “Slinky-whistler dispersion relation from ‘scaling’
,” Am. J. Phys.
58
, 916
–917
(1990
).10.
R. A.
Young
, “Longitudinal standing waves on a vertically suspended slinky
,” Am. J. Phys.
61
, 353
–360
(1993
).11.
J.
Dickerson
, H. M.
Kim
, and B.
Kosko
, “Fuzzy control for platoons of smart cars
,” Proceedings of the Third IEEE Conference on Fuzzy Systems
, Orlando, FL, 1994
, pp. 1632
–1637
.12.
S. -N.
Huang
and W.
Ren
, “Design of vehicle following control systems with actuator delays
,” Int. J. Syst. Sci.
28
, 145
–151
(1997
).13.
14.
H.
Goldstein
, C. P.
Poole
, and J. L.
Safko
, Classical Mechanics
, 3rd ed. (Addison-Wesley
, Reading, MA
, 2001
).15.
16.
W. H.
Press
, B. P.
Flannery
, S. A.
Teukolsky
, and W. T.
Vetterling
, Numerical Recipes
(Cambridge U. P.
, Cambridge
, 1986
).© 2010 American Association of Physics Teachers.
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