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Unformatted text preview: HW-12 1.In the complex notation there is a clever device for finding the time average of a product. Suppose )cos(),(atrkAtrfand )cos(),(btrkBtrg. Show that *)~~Re()2/1(gffg, where f~and g~are the complex of fand gand the star denotes complex conjugation. Solution:First, let us perform a direct calculation fgdtTfgT1where 2Tis the periodicity. )cos(2)]cos([2)]cos()22[cos(2)cos()cos(11babababaTbaTTABTTABdttrkTABdttrkBtrkATfgdtTfgSecond, let us calculate*)~~Re(gf. )exp(~),exp(~batrkBgtrkAf. Then )cos()](exp[Re)](exp[)](exp[Re*)~~Re(bbbbbbABiABtrkiBtrkiAgf. Therefore *)~~Re()2/1(gffgThis result can be applied to calculate many physical quantities such as the energy density and the Poynting vector....
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This note was uploaded on 02/06/2010 for the course PHYSICS 11 taught by Professor Qiu during the Fall '09 term at University of California, Berkeley.
- Fall '09