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Homework Help: Laplace Transform L[x(t)] given, find L[tx(t)]

  1. Nov 12, 2014 #1
    1. The problem statement, all variables and given/known data

    If L[x(t)] = (s + 4)/(s2 + 1), find L[tx(t)]

    2. Relevant equations
    Laplace transform:

    F(s) = 0∫ f(t)e-stdt

    Laplace table
    3. The attempt at a solution
    Clearly it's not just asking for a Laplace transform. Not sure what it's specifically asking to be honest.

    t multiplied by whatever is inside the equation definitely isn't the answer.
  2. jcsd
  3. Nov 12, 2014 #2


    Staff: Mentor

    Clearly it is. There are a couple of approaches you could take, but I'd like to see what you have tried before I share them with you.
    I don't know what this means...
  4. Nov 12, 2014 #3


    Staff: Mentor

    Is it asking for the Laplace transform of the function ##t x(t)## (i.e., the function obtained by multiplying ##x(t)## by ##t##), given the Laplace transform of ##x(t)##? That's what it looks like to me, but I'd like to make sure you have transcribed the problem statement correctly.

    Also, please show us explicitly your attempt at a solution(i.e., with equations showing the steps of the calculation you attempted). Just describing it in words isn't enough.
  5. Nov 14, 2014 #4
    Okay, there seems to be one property that sticks out for this:

    L[tf(t)] = -dF(s)/ds

    L[x(t)] = (s+4)/(s2 + 1)

    L[f(t)] = (s+4)/(s2 + 1). Then find L[tf(t)]

    $$\frac{d} {ds} [\frac {s+4} {s^2 + 1}] $$

    Just this derivative?

    = (d/ds)[(s+4)/(s2 + 1)-1]

    $$ \frac {(1)(s^2 + 1) - (2s)(s+4)} {{(s^2 + 1)}^2} $$

    Would I need only simplify the rest of this to get L[tx(t)] ?
  6. Nov 14, 2014 #5


    Staff: Mentor

  7. Nov 14, 2014 #6
    Okay, thanks! :)

    Edit: Oh wait I forgot that there was a negative sign by the derivative, so

    (s2 + 8s - 1)/(s2 + 1)2
    Last edited: Nov 14, 2014
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