Re: [理工] [工數]100年交大光電工數
看板Grad-ProbAsk作者ntust661 (Enstchuldigung~)時間15年前 (2011/03/21 19:57)推噓3(3推 0噓 2→)留言5則, 3人參與討論串2/2 (看更多)
※ 引述《sea1985 (我要變強>"<)》之銘言：
: Laplace transform is always used by poeple to find a solution in differential
: equation. If we define Laplace transform of fuction f(t) as L[f(t)]=F(s),
: and now we know F(s)=(1/s)tanhs,please (a)find fuction of f(t),whuch is the
: inverse Laplace transform of F(s),and (b) plot this function of f(t)
: 想知道這題的反拉結果會是什麼?
s -s
e - e
tanhs = ────────
e^s + e^-s
s
1 2 e
=> ── [ -1 + ────── ]
s e^s + e^-s
1 2
= ── [ -1 + ──────]
s 1 + e^-2s
-2s
for e < 1
1 -2s -4s -6s
= ── [ -1 + 2( 1 - e + e - e + ... ) ]
s
1 2 2s 4s
= ── - ── [ 1 - e + e - ...]
s s
= -H(t) + 2 [ H(t) - H(t-2) + H(t-4) - H(t-6) + ... ]
方波，振幅 1 , 週期 4 sec
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推
03/21 21:20, , 1F
03/21 21:20, 1F
推
03/22 00:36, , 2F
03/22 00:36, 2F
→
03/22 00:37, , 3F
03/22 00:37, 3F
→
03/22 00:39, , 4F
03/22 00:39, 4F
推
03/23 00:47, , 5F
03/23 00:47, 5F
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