Re: [理工] [工數]-拉式轉換
※ 引述《mdpming (阿阿 要加油)》之銘言：
: 1.
: 3
: -1 s
: L [ ---------- ]
: 4 4
: s + 4a
3
-1 s
L [ ---------- ]
4 4
s + 4a
1 a+i∞ s^3 e^st
=------∫ -----------ds
2πi a-i∞ s^4+4a^4
z^3e^zt
F(z)=--------
z^4+4a^4
∮F(z)dz=∫F(z)dz+∫F(z)dz+∫F(z)dz
c L1+L2 c' L
c:L1+L2+c'+L
=0+∫F(z)dz
L
=2πiRezF(z)
pole:z^4=-4a^4
z=√2ae^(j(π+2nπ)/4) n=0,1,2,3
=a(1+i),a(-1+i),a(-1-i),a(1-i)
=bi,i=1,2,3,4
z^3e^zt
->Rez(Fz,bi)=lim (z-bi)---------
z->bi z^4+4a^4
e^zt
=lim ---------
z->bi 4
1
RezF(z)=---(e^(a(1+j)t+e^(a(-1+j)t+e^(a(-1-j)t+e^(a(1-j)t)
4
1
=---(e^at+e^-at)(e^jat+e^-jt)
4
=coshatcosat
1 a+i∞ s^3 e^st
∴------∫ -----------ds
2πi a-i∞ s^4+4a^4
=coshatcosat
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◆ From: 123.193.214.165
※ 編輯: iyenn 來自: 123.193.214.165 (02/01 14:27)
推
02/01 15:35, , 1F
02/01 15:35, 1F
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02/01 15:37, , 2F
02/01 15:37, 2F
→
02/01 17:06, , 3F
02/01 17:06, 3F
推
02/01 17:10, , 4F
02/01 17:10, 4F
推
02/01 17:23, , 5F
02/01 17:23, 5F
→
02/01 20:36, , 6F
02/01 20:36, 6F
推
02/01 21:04, , 7F
02/01 21:04, 7F
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