Re: [理工] [工數]-拉式 ....怪怪的?
※ 引述《topee (eason)》之銘言：
: y"-4y'+5y=f(t) y(0)=0 y'(0)=1
: 0 t<1
: f(t) = ｛1 1<t<2
: 0 t>2
: f(t)= [u(t-1)-u(t-2)]1
: 令Y= L[y]
: L[y"]-4L[y']+5L[y] = e^-s L[1] -e^-2s L[1]
: t=t-1 t=t-2
: 1 1
: (s^2-4s+5)Y= 1 + ---e^-1s + ---e^-2s
: s s
1 1 1 1 s-4
Y= ---------- +( --- ---- - --- -----------)[e^-s - e^-2s]
(s-2)^2+1 5 s 5 s^2-4s+5
1 1 1 s 1
= ---------- + [---( --- - --------- - 4----------)](e^-s - e^-2s)
(s-2)^2+1 5 s (s-2)^2+1 (s-2)^2+1
1
y = e^2tsint +u(t-1)[---e^2t(-cost- 4sint)] -u(t-2)[]
5 t=t-1 t=t-2
這樣?
之後該怎麼分解 我又一頭霧水...
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