HomeWork5 - Home Work#5 Evaluate 29 P x as a Fourier series...

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Unformatted text preview: Home Work #5 Evaluate ( 29 P x as a Fourier series expression for the followings: x x a a P a c R P c- = c P a c c a a c a a c R P c- = ( 29 a ( 29 b 1 c c P Solution, Fourier series (a) The loading is an even function ⇒ ( 29 0, 0 from def., Eq. 3-21 , n B A a = = = l ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 cos cos 2 cos cos 2 sin sin 2 sin sin 2 sin a n a c a a c a a c a c n x n x A f x dx f x dx a a a c n x n x P dx P dx a a c a a c a n x a n x P P a n a c n a a c a n a n P a c P a c a n a c n a Pa n a c cn a π π π π π π π π π π π π π π---- = =- = +- - =- - =- +- =- = ∫ ∫ ∫ ∫ l l l ( 29 1 2 sin cos cos sin 2 1 sin n Pa n c n c n n cn a a Pa n c cn a π π π π π π π- - = - Hence, ( 29 ( 29 1 1 2 1 1 sin cos 2 1 2 2 1 3 3 1 4 4 sin cos sin cos sin cos sin cos . . ....
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This note was uploaded on 09/24/2011 for the course CIVL 7690 taught by Professor Staff during the Summer '10 term at Auburn University.

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HomeWork5 - Home Work#5 Evaluate 29 P x as a Fourier series...

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