Pendulum on a massive cord

Montgomery, C. G.

doi:10.1119/1.11335

Cited by 2 publications

(2 citation statements)

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“…Solving equations ( 7) and ( 9) and using Bessel function identities as in [3], one finds that solutions exist only when…”

Section: Theorymentioning

confidence: 99%

“…He approached the problem as the limiting case of a hanging chain and the resulting solutions involve what we now know as Bessel functions. Solutions to the problem with a point tip mass attached appear to be considered only much more recently and though solutions can be expressed using simple exact relationships between Bessel functions, the results must ultimately be determined either numerically [2], using approximations and the variational principle [3] or are derived approximately for limiting cases. In the latter case, this has been done to determine the correction to the lowest frequency mode, the pendulum mode, in the limit of a heavy tip mass [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The hanging cord with a real tip mass

Deschaine¹,

Suits²

2008

Eur. J. Phys.

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Normal mode solutions for the perfectly flexible hanging cord problem have been known for over 200 years. More recently, theoretical results for a hanging cord with a point mass attached were presented. Here the theoretical results are tested experimentally using high-precision techniques which are accessible for use in an introductory laboratory. Also included is a generalization of the theory for the case where the rotational inertia of the tip mass is not negligible. An exact expression is obtained which can be solved for the normal mode frequencies. In all cases, the theoretical results are in good agreement with experimental results. Both the theory and experiment are at a level accessible to upper level undergraduate physics students. The problem serves as an example of other problems involving one-dimensional wave propagation with a spatially dependent wave speed resulting in non-harmonic normal mode frequencies.

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“…Solving equations ( 7) and ( 9) and using Bessel function identities as in [3], one finds that solutions exist only when…”

Section: Theorymentioning

confidence: 99%