推 Gindaco:強 這題沒做出來...... 03/21 21:20
推 G41271:所以方波的拉式是tanhs , 基本波形要背. 03/22 00:36
→ G41271:方波呀 三角波 sin波 全波整流 半波整流 03/22 00:37
→ G41271:二樓沒看清楚 是tanhs/s 03/22 00:39
推 sea1985:thank you ^_^ 03/23 00:47
※ 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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