Re: [理工] [拉式] 98南交工數

[ejialan (eji)]

※ 引述《jerrysimon ()》之銘言：
: http://0pics.com/images/image171.jpg
: 第18題，我原本想要直接分式，但發現很難做
: 然後我讓它等於2式相乘、使用摺積定理，但逆轉換後的摺積我不會做
: 請問有人知道這題該怎麼處理嗎?
: 感謝~m(_ _)m~

Y(s) = 4/(s^2+1)^2/(s-1)^2

= (As+B)/(s^2+1)^2 + (Cs+D)/(s^2+1) + E/(s-1)^2 + F/(s-1)

As+B = [Y*(s^2+1)^2] | s^2=-1

     = [4/(s^2-2s+1)] | s^2=-1

     = 4/(-2s) | s^2=-1

     = 4s/(-2s^2) | s^2=-1

     = 2s => A=2, B=0

[Y*(s^2+1)^2]_s | s^2=-1          (_s表示對s微分)

= -8/(s-1)^3 | s^2=-1

= -8/(s^3-3s^2+3s-1) | s^2=-1

= -8/(-s+3+3s-1) = -4/(s+1)

= -4(s-1)/(s^2-1) | s^2=-1 = 2s-2 = A + 2s * (Cs+D) | s^2=-1

= A + 2Ds -2C => D=1, C=2

E = [Y*(s-1)^2] | s=1

  = 4/(s^2+1)^2 | s=1

  = 1

F = [Y*(s-1)^2]_s | s=1          (_s表示對s微分)

  = -16s/(s^2+1)^3 | s=1

  = -2

Y(s) = 2s/(s^2+1)^2 + 2s/(s^2+1) + 1/(s^2+1) + 1/(s-1)^2 -2/(s-1)

y(t) = tsin(t) + 2cos(t) + sin(t) + te^t - 2e^t

答案選(A)

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推 squallting:這一題反拉太慢 才7分而已~"~
推 blazesunny:太厲害了推!
推 a149851571:打鐘摟XDDD
推 cg1436:這題7分真的會做不下去...
推 jack0711:最後的Y(s)好像不等於題目的Y(s),是我看錯嗎@@??
推 jack0711:我看錯了SORRY@@
推 mp8113f:不符合投資報酬率啊 ...XD" 這樣搞下去 ...
推 ntust661:才兩個項 其實只微分一次都算還好@@
推 jerrysimon:請問2s-2 = A + 2s * (Cs+D) ←這條等式是怎麼來的?
推 jerrysimon:我以為Cs+D就=2s-2耶
→ ejialan:As+B微分跑出A (Cs+D)(s^2+1)微分跑出C(s^2+1)+2s(Cs+D)
→ ejialan:其他兩項微分都有(s^2+1)會消掉
→ sneak: As+B微分跑出A ( https://daxiv.com