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Laplace Transformation of 2nd order step function

  1. Nov 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the Laplace transform of f(t) where
    f(t)={ 3 if 0<=t<2
    2t^2+2 if 2<=t<3
    -4 if t>=3


    2. Relevant equations



    3. The attempt at a solution
    We where taught to approach this from a "turn-off, turn-on" strategy where
    f(t)=3-3(u2)+(2t^2+t)u2-(2t^2+t)u3-4u3
    you then group together the u2 and u3 terms to get
    3+(2t^2+t-3)u2- (2t^2+t+4)u3
    in the past from this step you try and get what's being multiplied by u2 and u3 in terms of (t-3) and (t-2) respectively. and then take the Laplace transform of it as though the (t-3) and (t-2) term was just t. where u2 becomes e^2t and u3 becomes e^3t. but with 2t^2 I don't know what to do. Can you help please!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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