example_IV_2_01 - Example IV.2.1 Find the particular...

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Example IV.2.1 Find the particular solution of the EOM for the system shown below for a=T/2 . f(t) F 0 -a/2 a/2 T Fourier Series f t ( ) = f 0 + f cj cos j Ω t + f sj sin j Ω t [ ] j = 1 where Ω = 2 π /T and f 0 = 1 T f t ( ) dt T/2 T/2 = 1 T f t ( ) dt T/2 a/2 + f t ( ) dt a/2 a/2 + f t ( ) dt a/2 T/2 = 1 T 0dt T/2 a/2 + F 0 dt a/2 a/2 + 0dt a/2 T/2 = 1 T F 0 a 2 a 2 = a T F 0
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f cj = 2 T f t ( ) cos j Ω t ( ) dt T/2 T/2 = 2 T f t ( ) cos j Ω t ( ) dt T/2 a/2 + f t ( ) cos j Ω t ( ) a/2 a/2 + f t ( ) cos j Ω t ( ) dt a/2 T/2 = 2 T 0dt T/2 a/2 + F 0 cos j Ω t ( ) dt a/2 a/2 + 0dt a/2 T/2 = 2 T F 0 sin j Ω t ( ) j Ω t = a/2 t = a/2 = 2 T F 0 2sin j Ω a/ 2 ( ) j Ω = 2F
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example_IV_2_01 - Example IV.2.1 Find the particular...

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