Review of approximate equations for the pendulum period
Precision measurements of the pendulum period as a function of the amplitude can now be made with a variety of instruments including MEMs gyro/accelerometers, and thus theoretical expressions are required for comparison. Unfortunately exact solution of the pendulum equation involves elliptic integra...
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| Veröffentlicht in: | European journal of physics 2021-01, Vol.42 (1), p.15005, Article 015005 |
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| creator | Hinrichsen, Peter F |
| description | Precision measurements of the pendulum period as a function of the amplitude can now be made with a variety of instruments including MEMs gyro/accelerometers, and thus theoretical expressions are required for comparison. Unfortunately exact solution of the pendulum equation involves elliptic integrals, which cannot be expressed in terms of elementary functions, and therefore a wide variety of approximations have been published. These range from simple single-term formulae to more sophisticated equations, which apply to a wider range of amplitudes, to an iterative procedure for calculating the precise period. The published approximations are compared as Taylor series expansions, and graphically to indicate their accuracy and their regions of applicability. |
| doi_str_mv | 10.1088/1361-6404/abad10 |
| format | Article |
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J. Phys</addtitle><description>Precision measurements of the pendulum period as a function of the amplitude can now be made with a variety of instruments including MEMs gyro/accelerometers, and thus theoretical expressions are required for comparison. Unfortunately exact solution of the pendulum equation involves elliptic integrals, which cannot be expressed in terms of elementary functions, and therefore a wide variety of approximations have been published. These range from simple single-term formulae to more sophisticated equations, which apply to a wider range of amplitudes, to an iterative procedure for calculating the precise period. 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J. Phys</addtitle><date>2021-01-01</date><risdate>2021</risdate><volume>42</volume><issue>1</issue><spage>15005</spage><pages>15005-</pages><artnum>015005</artnum><issn>0143-0807</issn><eissn>1361-6404</eissn><coden>EJPHD4</coden><abstract>Precision measurements of the pendulum period as a function of the amplitude can now be made with a variety of instruments including MEMs gyro/accelerometers, and thus theoretical expressions are required for comparison. Unfortunately exact solution of the pendulum equation involves elliptic integrals, which cannot be expressed in terms of elementary functions, and therefore a wide variety of approximations have been published. These range from simple single-term formulae to more sophisticated equations, which apply to a wider range of amplitudes, to an iterative procedure for calculating the precise period. 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| language | eng |
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| source | IOP Publishing Journals; Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" />; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | Education & Educational Research Education, Scientific Disciplines large amplitude pendulum pendulum period approximations Physical Sciences Physics Physics, Multidisciplinary Science & Technology simple and compound pendulum Social Sciences |
| title | Review of approximate equations for the pendulum period |
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