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The hanging cord with a real tip mass

J. S. Deschaine and B. H. Suits

**Abstract**

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 incluced 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 lundergraduate 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.

European Journal of Physics **29**, 1211-1222 (2008).

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