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Unit step function transform

  1. Aug 14, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the laplace transform of u(-t)


    2. Relevant equations



    3. The attempt at a solution
    For u(t), the laplace transform of it is 1/s, basically taking the integral of e^-st from 0 to infinity.

    In this case, since the unit step function approaches from the negative side, do I just take the integral of e^(-st), but switch the limit (from infinity to 0) for the purpose of transformation, leaving with -1/s?
     
  2. jcsd
  3. Aug 14, 2007 #2

    learningphysics

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    What is the value of u(-t) for t>0... what does that say about the integral of u(-t)*[e^(-st)]?
     
  4. Aug 14, 2007 #3
    u(-t) for t > 0 is equal to 0, does that immediately lead to the conclusion that the transformation of u(-t) = 0? What if t < 0?
     
  5. Aug 14, 2007 #4

    learningphysics

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    Yes, though a function can be 0 for t>0, but still have non-zero laplace transform... like the unit impulse function... but that's because the value at 0 is infinite... the laplace transform is defined from 0- (a value slightly less than 0) to infinity to include what happens at t=0... what happens for t<0 doesn't matter... but what happens at zero does matter.

    But for u(-t) the value at t=0 is finite... so the integral is 0.

    Hope I'm not missing anything... I think this is all true...

    This is all for one-sided laplace transforms... two-sided is different...
     
    Last edited: Aug 14, 2007
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