Laplace from first principles

  • Thread starter NotStine
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  • #1
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Homework Statement



Find, from first principles, the Laplace transform of f(t) = sin2(3t)

Homework Equations



sin23t = 1/2(1-cost(6t))

L{SINat} = a/(s2 + a2)

The Attempt at a Solution



I already have the solution.

s/2(s2 + 36)

What I want to ask is what does the first principles part mean? Is that asking me to integrate or look at the table of transforms? I don't quite understand what method I'm suppose to use for the transformation. Any light on this topic would be heavily appreciated.
 
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Answers and Replies

  • #2
HallsofIvy
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The Laplace transform of a function, f(x) is defined as
[tex]L(f)(s)= \int_0^\infty e^{-sx}f(x)dx[/tex]
"From first principles" means using that formula. I recommend integrating by parts.
 
  • #3
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I see. That makes sense.

Thank you very much for your help.
 

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