Fourier Series Pt 2

# Fourier Series Pt 2 - University of Waterloo CivE 331...

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Unformatted text preview: University of Waterloo CivE 331 Consider the following function, which could represent ramp loading with decay: x +1 ; 0 < x < 4 f (x ) = -k ( x - 4 ) where ; 4< x <L 5e is a degradation constant. Graphically, ( ) with = 0.26824 and = 10 is: 6.00 5.00 4.00 3.00 2.00 1.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 is needed if ( ) is to be expressed as a Since ( ) is defined over < < , a Fourier Series. The four important expansions are: (1) half-range cosine (HRC), (2) half-range sine (HRS), (3) quarter-range cosine (QRC), and (4) quarter-range sine (QRS). University of Waterloo CivE 331 6 5 4 3 2 1 0 -20 -16 -12 -8 -4 0 4 8 12 16 20 University of Waterloo CivE 331 -20 -16 -12 -8 -4 6 4 2 0 -2 -4 -6 0 4 8 12 16 20 University of Waterloo CivE 331 -20 -16 -12 -8 -4 6 4 2 0 -2 -4 -6 0 4 8 12 16 20 University of Waterloo CivE 331 -20 -16 -12 -8 6 4 2 0 -4 -2 0 -4 -6 4 8 12 16 20 ...
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## This document was uploaded on 02/09/2010.

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