[理工] [工數]-傅立葉級數
.1.find a formal fourier series solution of the endpoint value problem
x"+4x=4t x(0)=1 x(1)=0
n+1
∞ 1 4(-1)
答案 x=2Σ --------- [-------- - nπ] sin nπt
n=1 4-n^2π^2 nπ
2.x(t)=1 -0.5 <t<0.5 x(t)=0 otherwise
∞ sinwcos(2w)
find S ------------dw
-∞ w
答案 0
3.x(t)=∣t-1∣ , 0<t<2 x(t+2)=x(t) ,expand into fourier series
∞ inwt ∞
x(t)= Σ Xn e = a0 +Σ an cosnwt +bn sinnwt
n=-∞ n=1
∞
find (1)Xn (2)an bn (3)Σ an cos(1/2)nw
n=1
1
答案(1)Xn=--------[1-cosnπ] , n≠0 X0=1/2 w=π
n^2π^2
2
(2)a0=1/2 ak=------- [1-cosnπ] , bn=0
n^2π^2
∞
(3) Σ an cos(1/2)nw=0
n=1
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※ 編輯: winer8 來自: 114.37.82.135 (01/02 17:29)
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