Re: [理工] [工數]-laplace

[iyenn (曉風)]

1.
let L(x(t))=X
             2      5
SX-1 + 3X + --- X= ---
             S      S

S^2+3S+2      5
---------X = ---- +1
  S           S
      5              S
X=----------- + ----------
  (s+1)(s+2)    (S+1)(S+2)

      1      -1       -1      2
X=5{-----+ ------}+{ -----+ -----}
    (s+1)  (s+2)     (S+1)  (S+2)


x(t)=L^-1(X)


    =5(e^-t - e^-2t)u(t)  -e^-t + 2e^-2t


2.         S
SY-1 + Y------- = e^-3s
        S^2 + 4

 S^3+4S+S
(----------)Y=e^-3s + 1
   S^2+4


   s^2 + 4            S^2+4
Y=----------e^-3s  + --------
  S(S^2 + 5)         S(S^2+5)

    4/5          (1/5)S                4/5     (1/5)S
 ={-------   +   ---------- ) e^-3s +{ ---- + ----------}
      S           S^2 + 5               S      S^2 + 5

    4      1                             4      1
y={---  + --- cos{5^1/2 (t-3) }u(t-3)+ {---  + --- cos(5^1/2 t )
    5      5                             5      5

有錯請不吝指教

--
電磁、電子、線代、工數

唸書唸得發了狂~歡迎討論,共勉之

http://www.facebook.com/home.php#/iyen.li

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 123.193.214.165
推 ooopppeeennn:3Q~
→ l1560ccdd:iy大大很厲害喔!! 也是應屆考生嗎 ??