The Slinky as a model for transverse waves in a tenuous plasma

Blake, J.; Smith, L. N.

doi:10.1119/1.11699

Cited by 5 publications

(5 citation statements)

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“…The physics of slinkies has attracted attention since their invention in 1943. Topics of studies include the hanging configuration of the slinky, 1,2 the ability of a slinky to walk down stairs, 3 the modes of oscillation of a vertically suspended slinky, 4,5 the dispersion of waves propagating along slinkies, [6][7][8] and the behavior of a vertically stretched slinky when it is dropped. [9][10][11] Slinkies are examples of tension springs, i.e.…”

Section: Introductionmentioning

confidence: 99%

Modeling a falling slinky

Cross

Wheatland

2012

American Journal of Physics

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A slinky is an example of a tension spring: in an unstretched state a slinky is collapsed, with turns touching, and a finite tension is required to separate the turns from this state. If a slinky is suspended from its top and stretched under gravity and then released, the bottom of the slinky does not begin to fall until the top section of the slinky, which collapses turn by turn from the top, collides with the bottom. The total collapse time t c (typically ∼ 0.3 s for real slinkies) corresponds to the time required for a wave front to propagate down the slinky to communicate the release of the top end. We present a modification to an existing model for a falling tension spring 9 and apply it to data from filmed drops of two real slinkies. The modification of the model is the inclusion

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Section: Introductionmentioning

confidence: 99%

Modeling a falling slinky

Cross

Wheatland

2012

American Journal of Physics

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“…Values of EA for each Slinky were obtained as described in section II, while EI values were obtained using Castigliano's method [52]. We plot n c versus n r , given by equation 17 Once a Slinky is stable in the shape of an arch, stability loss can occur if one end of the spring is lifted above a critical height, which we refer to as the step instability. Experimentally, we incrementally decreased y n relative to y 1 in a quasi-static manner (where the y axis is upward), and measured the critical displacement δ c = y 1 − y n as a function of the number of coils n (Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Mak [16] defined an effective mass with regard to the static elongation of the vertically suspended Slinky. Blake and Smith [17] and Vandergrift et al [18] suspended a Slinky horizontally by strings and investigated the behavior of transverse vibrations and waves. Longitudinal and transverse waves in a horizontal Slinky were examined by Gluck [12].…”

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confidence: 99%

Equilibria and instabilities of a Slinky: Discrete model

Holmes¹,

Borum²,

Moore³

et al. 2014

International Journal of Non-Linear Mechanics

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The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically nonlinear deformations from minimal applied forces. By considering it as a system of coils that act to resist axial, shearing, and rotational deformations, we develop a discretized model to predict the equilibrium configurations of a Slinky via the minimization of its potential energy. Careful consideration of the contact between coils enables this procedure to accurately describe the shape and stability of the Slinky under different modes of deformation. In addition, we provide simple geometric and material relations that describe a scaling of the general behavior of flexible, helical springs.The floppy nature of a tumbling Slinky (Poof-Slinky, Inc.) has captivated children and adults alike for over half a century. Highly flexible, the spring will walk down stairs, turn over in your hands, and -much to the chagrin of children everywhere -become easily entangled and permanently deformed. The Slinky can be used as an educational tool for demonstrating standing waves, and a structural inspiration due to its ability to extend many times beyond its initial length without imparting plastic strain on the material. Engineers have scaled the iconic spring up to the macroscale as a pedestrian bridge [1], and down to the nanoscale for use as conducting wires within flexible electronic devices [2,3], while animators have simulated its movements in a major motion picture [4]. Yet, perhaps the most recognizable and remarkable features of a Slinky are simply its ability to splay its helical coils into an arch ( Fig. 1), and to tumble over itself down a steep incline.A 1947 patent by Richard T. James for "Toy and process of use" [5] describes what became known as the Slinky, "a helical spring toy adapted to walk and oscillate." The patent discusses the geometrical features, such as a rectangular cross section with a width-to-thickness ratio of 4:1, compressed height approximately equal to the diameter, almost no pretensioning but adjacent turns (coils) that touch each other in the absence of external forces, and the ability to remain in an arch shape on a horizontal surface. In the same year, Cunningham [6] performed some tests and analysis of a steel Slinky tumbling down steps and down an inclined plane. His steel Slinky had 78 turns, a length of 6.3 cm, and an outside diameter of 7.3 cm. He examined the spring stiffness, the effects of different step heights and of inclinations of the plane, the time length per tumble and the corresponding angular velocity, and the velocity of longitudinal waves. He stated that the time period for a step height between 5 and 10 cm is almost independent of the height and is about 0.5 s. Forty years later, he gave a further description of waves in a tumbling Slinky [7]. Longuet-Higgins [8] also studied a Slinky tumbling down stairs. His phosphor-bronze Slinky had 89 turns, a length of 7.6 cm, and an outside diameter of 6.4 cm. In his analysis, he imagined the Slinky as an elastic fluid, with...

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“…A Slinky can also be used to demonstrate transverse waves and longitudinal waves depending on orientation and forcing conditions. 4 A Slinky can also descend stairs, the original behaviour described by Cunningham 5 and Wilson. 6 A Slinky has long been used in the education of early years undergraduate physicists demonstrating the phenomena discussed above.…”

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 94%

Lagrange's method applied to a Slinky

Cumber

2023

International Journal of Mechanical Engineering Education

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The Lagrange method is applied to two dynamic models of a Slinky, one based on point masses and linear springs and a second where the Slinky is represented as a sequence of half hoops connected by torsion springs. For the first time, the use of Lagrange's method applied to a Slinky has produced a multi-body dynamic model that can potentially with minor modification reproduce all the interesting behaviour Slinkies are well known for; descending stairs, pseudo levitation, transmission of longitudinal and transverse waves. In this paper, the models are derived and a limited exploration of the two dynamic models’ behaviour is considered. For unforced oscillation, the point mass model and torsion spring model produce a similar amplitude and frequency. When considering forced oscillations, the point mass model has a very different spectrum of natural frequencies than the torsion spring model. The torsion spring model is considered for different forcing conditions.

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The Slinky as a model for transverse waves in a tenuous plasma

Cited by 5 publications

References 0 publications

Modeling a falling slinky

Modeling a falling slinky

Equilibria and instabilities of a Slinky: Discrete model

Lagrange's method applied to a Slinky

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