推 kissboy1065:終於等到了 先謝謝在看^^ 03/27 22:41
※ 引述《kissboy1065 ( 川)》之銘言：
: (1) Find the laplace transfer X(s) of x(t) besure to eliminate Y(s) from
: expression
: (2) Find the solution y(t)
: dx/dt = 2x - 3y , x(0)=8
: dy/dt = -2x + y , y(0)=3
: 麻煩了謝謝
原聯立方程式取Laplace transform得
sX-x(0)=2X-3Y
sY-y(0)=-2X+Y
整理得
(s-2)X+3Y=8
2X+(s-1)Y=3
│s-2 3 │
Δ =│ │=(s-2)(s-1)-6=s^2-3s-4
│2 s-1│
│8 3 │
Δ =│ │=8(s-1)-9=8s-17
X │3 s-1│
│s-2 8│
Δ =│ │=3(s-2)-16=3s-22
Y │2 3│
8s-17 8(s-3/2)-5 8(s-3/2) 2*(5/2)
X = ──── = ──────── = ───────── - ─────────
s^2-3s-4 (s-3/2)^2 - 25/4 (s-3/2)^2 - (5/2)^2 (s-3/2)^2 - (5/2)^2
-1 (3/2)t
x(t)=L [X(s)] = [8cosh(5/2)t-2sinh(5/2)t]e
3s-22 3(s-3/2)-35/2 3(s-3/2) 7*(5/2)
Y = ──── = ──────── = ───────── - ─────────
s^2-3s-4 (s-3/2)^2 - 25/4 (s-3/2)^2 - (5/2)^2 (s-3/2)^2 - (5/2)^2
-1 (3/2)t
y(t)=L [Y(s)] = [3cosh(5/2)t-7sinh(5/2)t]e
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