Re: [理工] laplace 逆轉換
※ 引述《happy3512 (海陸5號)》之銘言：
: 2
: S
: ------------
: 2 2 2
: ( S + B )
: 這個的反轉換,想好久還是想不出來..
: 麻煩各位大大
1 (1/a)
─────── = ──────── = L { K(a) sin( w(a) t ) } = L{ f(t,a) }
a s^2 + B^2 s^2 + (B^2/a)
d - s^2
── L{ f(t,a) } = ─────────
da (a s^2 + B^2)^2
d
= L{── f }
da
1 √a 1
K = ── ( ─── ) = ────
a B √a B
B
w = ───
√a
d
── f = K'(a) sin( w(a) t ) + K cos( w(a) t ) w'(a) t
da
-1 t -B
= ────── sin(wt) + ──── cos( wt ) ────
2 √a a B √a B 2 √a a
看看 a = 1 吧 ~
-s^2 1 t
─────── = - ── sinBt - ── cosBt
(s^2 + B^2)^2 2B 2
So...
s^2 1 t
─────── = ── sinBt ── cosBt
(s^2 + B^2)^2 2B 2
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※ 編輯: ntust661 來自: 140.112.16.74 (10/18 20:27)
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