View source for Characteristic-value problem



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== characteristic-value problem ==
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<div class="definition"><div class="short_definition">A problem in which an undetermined [[parameter]] is involved in the  coefficients of a differential equation and in which the solution of the differential equation, with  associated [[boundary conditions]], exists only for certain discrete values of the parameter, called  [[eigenvalues]] (or characteristic values, sometimes principal values).</div><br/> <div class="paragraph">An important example of a physical problem that leads to a characteristic-value problem is the  determination of the modes and frequencies of a vibrating system. In this case the [[dependent variable|dependent  variable]] of the differential equation represents the displacements of the system and the parameter  represents the frequencies of vibration.</div><br/> </div>
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