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Oscillations

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Abstract

In § 6·32 we considered the differential equation ẍ + n2x = 0 and showed that its general solution may be any of the forms
$$ \begin{array}{*{20}{c}} {x = A\;\cos \;nt\; + \;B\;\sin \;nt} \\ {x = \;P\;\cos \;\left( {nt + \alpha } \right)} \\ {x = P\;\sin \;\left( {nt + \beta } \right)} \end{array} $$
where A, B, P, α, β are arbitrary constants. If x is a co-ordinate measured from the centre of oscillation and t is a measure of time, then either the differential equation or one of the solution forms may be taken as a definition of a simple harmonic oscillation of period 2π/n. The amplitude and phase constants are arbitrary.

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Copyright information

© H. J. Halstead and D. A. Harris 1963

Authors and Affiliations

  1. 1.Mathematics DepartmentRoyal Melbourne Institute of TechnologyAustralia

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