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February 20th, 2017, 12:37 AM  #1 
Newbie Joined: Feb 2017 From: malaysia Posts: 1 Thanks: 0  Finding laplace transform of unit step function?
The initial function is: f(t) = 0 for 0<t<1 1 for 1<t<2 0 for >2 In function notation this function would be f(t)=U(t)U(t2). However the actual question is for us to find f(t1). So what would this mean? Would it mean: f(t) = 1 for 0<t<1 0 for 1<t<2 1 for >2 or something else? 
February 20th, 2017, 03:23 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,454 Thanks: 489 Math Focus: Yet to find out. 
If $f(t) = U(t)  U(t  2)$, then, $f(t  1) = U(t  1)  U((t  1)  2) = U(t  1)  U(t  3)$. Hence, $\displaystyle f(t  1) = $$\displaystyle \left\{ \begin{array}{rl} 1, &\mbox{1 $\displaystyle \leq$ t < 3} \\ 0, &\mbox{elsewhere.} \end{array} \right. $ The Laplace Transform of $f(t  1)$ should be straight forward to compute using tables or otherwise. 

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finding, function, laplace, step, transform, unit 
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