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5 - Integration

Published online by Cambridge University Press:  02 April 2020

Joel Franklin
Joel Franklin
Affiliation:
Reed College, Oregon
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Summary

With many physical applications already on the table, in this chapter, we return to some of the simplified ones and re-complexify them.These problems require more sophisticated, and incomplete, solutions.Instead of finding the position of the bob for the simple pendulum, we find the period of motion for the ``real" pendulum.Instead of the classical harmonic oscillator, with its familiar solution, we study the period of the relativistic harmonic oscillator, and find that in the high energy limit, a mass attached to a spring behaves very differently from its non-relativistic counterpart.

Keywords

Integral solutionsChange of variablesSubstitutionIntegration by partsPeriodPerimeterRelativistic oscillator
Type
Chapter
Information
Mathematical Methods for Oscillations and Waves , pp. 120 - 145
Publisher: Cambridge University Press
Print publication year: 2020

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  • Integration
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.007
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  • Integration
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Integration
  • Joel Franklin, Reed College, Oregon
  • Book: Mathematical Methods for Oscillations and Waves
  • Online publication: 02 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108769228.007
Available formats
×