Waggling pendulums and visualization in mechanics

Cumber, Peter Stewart

doi:10.1080/0020739x.2014.987838

Cited by 7 publications

(2 citation statements)

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“…In this paper, nonideal elastic deformation is modelled by changing the equations of motion to This is the simplest way of introducing dissipation into the system and has been used successfully to model frictional losses at a pivot. 18 Within the context of the torsion spring model, it can be thought of as frictional loss within the torsional springs. Note the constant C D is a parameter being used to make the numerical solution of the equations of motion slightly dissipative and hence numerically stable.…”

Section: Vertical Motion Of a Slinkymentioning

confidence: 99%

“…One option is to implement dynamic models, embedded in a virtual learning environment (VLE). 15–18 Equipped with a VLE the student can explore parameter space without initially having a grasp of the mathematical basis of the dynamic model. The argument being the student can grasp the mathematical basis once they have insight into the dynamic behaviour.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Vertical Motion Of a Slinkymentioning

confidence: 99%