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20 - Normal modes

Published online by Cambridge University Press:  05 June 2012

Roel Snieder
Affiliation:
Colorado School of Mines
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Summary

Many physical systems have the property that they can carry out oscillations at certain specific frequencies only. As a child (and hopefully also as an adult) you will have discovered that a swing in a playground will move only with a specific natural period, and that the force that pushes the swing is only effective when the period of the force matches the period of the swing. The patterns of motion at which a system oscillates are called the normal modes of the system. A swing has one normal mode, but you have seen in Section 13.6 that a simple model of a tri-atomic molecule has three normal modes. An example of a normal mode of a system is given in Figure 20.1 which shows the pattern of oscillation of a metal plate which is driven by an oscillator at a fixed frequency. The screw in the middle of the plate shows the point at which the force on the plate is applied. Sand is sprinkled on the plate. When the frequency of the external force is equal to the frequency of a normal mode of the plate, the motion of the plate is given by the motion that corresponds to that specific normal mode. Such a pattern of oscillation has nodal lines where the motion vanishes. These nodal lines are visible because the sand on the plate collects at these lines.

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Chapter
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A Guided Tour of Mathematical Methods
For the Physical Sciences
, pp. 311 - 352
Publisher: Cambridge University Press
Print publication year: 2004

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  • Normal modes
  • Roel Snieder, Colorado School of Mines
  • Book: A Guided Tour of Mathematical Methods
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511983962.021
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  • Normal modes
  • Roel Snieder, Colorado School of Mines
  • Book: A Guided Tour of Mathematical Methods
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511983962.021
Available formats
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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.

  • Normal modes
  • Roel Snieder, Colorado School of Mines
  • Book: A Guided Tour of Mathematical Methods
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511983962.021
Available formats
×