[理工] [工數]-拉氏題目-請高手幫看一下
不知道做錯 還是對 後面就不會了
題目:
y"+5y'+6y=f(t) y(0)=y'(0)=0
f(t)={ -2 for 0≦ t< 3
0 for t≧3
------------------------------------------
f(t)= u(t)-u(t-3)(-2)
1 1
= ---e^0s － ---e^-3s(-2)
s s
1
= ---(e^0s ＋ 2e^-3s)
s
[s^2Y － sy(0) － y'(0)]＋ 5[sY － y(0)]＋ 6Y
1 1
(s^2＋5s＋6)Y = ---e^0s － ---e^-3s(-2)
s s
1 1
Y = --------- ╳ ---(e^0s ＋ 2e^-3s)
s^2+5s+6 s
1 1 A Bs+C
--- ╳ -------- = --- ＋ ----------
s s^2+5s+6 s (s^2+2s+6)
1 1 5
A= --- B= － --- C= － ---
6 6 6
1 1 1 s 5
= ｛--- ╳ --- － ---( -------- ＋ ---------- )｝ ╳ (e^0s ＋ 2e^-3s)
6 s 6 s^2+2s+6 s^2+2s+6
跪求幫解
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