Fourier Series

Fourier Series - CE 573: Structural Dynamics Fourier Series...

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Unformatted text preview: CE 573: Structural Dynamics Fourier Series Example 0 t 2 sec 0 lb F (t ) = , F (t + 5) = F (t ) 200 lb 2 t 5 sec rad T = 5 seconds =2 /5 sec . Constant term: ao = = 1 5 sec 1 2 sec 1 5 sec F (t ) dt = ( 0 lb ) dt + ( 200 lb ) dt 5 sec 5 sec 5 sec 2 0 0 sec 1 {( 200 lb )( 5 sec - 2 sec )} = 120 lb. 5 sec Cosine term: an = 25 25 2 nt 2 nt F (t ) cos dt = ( 200 lb ) cos dt 50 52 5 5 t =5 5 200 4 n 2 nt = ( 80 lb ) sin sin = lb. n 5 2 n 5 t = 2 Sine term: bn = 25 200 4 n 2 nt F (t )sin 5 dt = n cos 5 - 1 lb. 50 Approximation: 200 N 1 4 n 2 nt 1 4 n 2 nt F (t ) 120 lb + lb - sin cos + cos - 1 sin n =1 n 5 5 n 5 5 ...
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Fourier Series - CE 573: Structural Dynamics Fourier Series...

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