[理工] [工數]-喻超凡工程數學第十一章LAPLACE轉換
此題為交大機械丙某年的考題
求以下的拉式轉換
︴0 t<0
f(t)＝ ︴1 nc≦ t ≦(n+1)c for n=0,2,4…,f(t+2c)=f(t).
︴-1 (n+1)c< t < (n+2)c
正解:(1-e^(-sc))/[s(1+e^(-sc))]
小弟的解法如下，不知道哪裡有算錯，跟正解答案不同，也對正解答案有疑慮。請高手教
導我這一題，感激不盡。
sol:
∵f(t)要為片段且連續，故令n=0
c 2c
L{f(t)}=∫ 1e^(-st)dt + ∫ -1e^(-st)dt
0 c
| c | 2c
=[-(1/s)e^(-st)]| + [(1/s)e^(-st)]|
| 0 | c
=(1/s)×[1-e^(-sc)]^2
以上是小弟的算式，拜託各位高手解惑了，謝謝!
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