- #1
Juanriq
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Homework Statement
I'm trying to take the laplace transfrom of [itex] t H(t) [/itex] where H(t) is the unit step function. Also, in a separate problem I get [itex] e^{-t} H(t) - e^{-t}H(t-1) [/itex] and I am wondering how to manipulate it properly
Homework Equations
[itex] L \{ f(t-a) H(t-a) \} = e^{as}F(s) [/itex]The Attempt at a Solution
For the first part, I thought that [itex] L \{ t H(t) \}[/itex] should just give [itex] \frac{1}{s^2} [/itex] back out, but the answer key in the book I'm using says that it is just [itex] \frac{1}{s} [/itex].For the second part of my question, I know we have to manipulate the exponential, but how would I manipulate them? For instance, I want [itex] e^{t}H(t) [/itex], but can't I only multiply by a constant? Obviously [itex] e^{-t}e^{2t}H(t) [/itex] would do what I want, but now I'm introuducing something I can't factor outside the transform. Similarly for the second, [itex] e^{2t-1}e^{-t} [\latex] would do the trick... Any help is appreciated!