Difference between revisions of "Frequency Domain Problem"
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This is closely connected with the [[Fourier Transform in Time]]. Essentially after this | This is closely connected with the [[Fourier Transform in Time]]. Essentially after this | ||
| − | we are left we a problem in which all time dependence is proportional to <math> | + | we are left we a problem in which all time dependence is proportional to <math>\exp (i\omega t)</math> |
and the resultant problem (for complex valued potential, displacement etc.) | and the resultant problem (for complex valued potential, displacement etc.) | ||
is said to be in the frequency domain (as opposed to the time domain). | is said to be in the frequency domain (as opposed to the time domain). | ||
In many practical applications this is the only solution required. i.e. engineers simply want | In many practical applications this is the only solution required. i.e. engineers simply want | ||
| − | a table of force as a function of frequency. | + | a table of force as a function of frequency. Often the dependence is taken as |
| + | <math>\exp (-i\omega t)</math> | ||
[[Category:Linear Water-Wave Theory]] | [[Category:Linear Water-Wave Theory]] | ||
Revision as of 22:55, 16 December 2006
This is closely connected with the Fourier Transform in Time. Essentially after this we are left we a problem in which all time dependence is proportional to [math]\displaystyle{ \exp (i\omega t) }[/math] and the resultant problem (for complex valued potential, displacement etc.) is said to be in the frequency domain (as opposed to the time domain). In many practical applications this is the only solution required. i.e. engineers simply want a table of force as a function of frequency. Often the dependence is taken as [math]\displaystyle{ \exp (-i\omega t) }[/math]
