※ 引述《lau245021 (月詩)》之銘言:
: 6.F(s)=(8-4s)/(s^2 +1)[(s-1)^2 +4] + (s+1)/(s-1)^2+4
: 這題算到這就卡住了 不會逆回去= =
: 拜託各位高手了 期末考要到了.... 努力中...
: 小弟程度不是很好 算式拜託 詳細一點^^~
-4s+8 As+B Cs+D
令 ───────── = ──── + ──────
(s^2 +1)[(s-1)^2 +4] s^2 +1 (s-1)^2 +4
兩邊去分母得
-4s+8 = (As+B)[(s-1)^2 +4]+(Cs+D)(s^2 +1)
= (As+B)(s^2-2s+5)+Cs^3+Cs+Ds^2+D
= As^3-2As^2+5As+Bs^2-2Bs+5B+Cs^3+Cs+Ds^2+D
= (A+C)s^3+(-2A+B+D)s^2+(5A-2B+C)s+(5B+D)
比較係數得
A+C = 0 A = 0
-2A+B+D = 0 解得 B = 2
5A-2B+C = -4 C = 0
5B+D = 8 D = -2
所以
0s+2 0s-2 s+1
F(s)= ──── + ────── + ─────
s^2 +1 (s-1)^2 +4 (s-1)^2 +4
2 s-1
= ──── + ──────
s^2 +1 (s-1)^2 +4
-1
f(t)=£ [F(s)]= 2sin(t)+(e^t)cot(2t)
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