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Laplace (heaviside function)

  1. Nov 8, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the Laplace of the piecwise continuous function:
    F(t)= t (when t<2)
    = 8-3t (when 2<=t<3)
    = t-4 ( when 3<=t<4)
    = 0 (when 4<=t)

    2. Relevant equations

    I want to use the heaviside function to see if i can apply it to other questions

    3. The attempt at a solution

    = t[H(t)] - t[H(t-2)] + (8-3t)[H(t-2)] - (8-3t)[H(t-3)] + (t-4)[H(t-3)] - (t-4)[H(t-4)]

    Does this then equal to: Laplace of t times laplace of H(t) -lap(t)times(lap(H(t-2)) + etc...

    because i did this but i got the wrong answer, i think im missing something.

    Thank you.
  2. jcsd
  3. Nov 8, 2008 #2


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    Homework Helper
    Gold Member

    To start with, [tex]-tH(t-2)= \left\{ \begin{array}{lr} 0, & t<2 \\ -t, & t \geq 2 \end{array} \neq \left\{ \begin{array}{lr} t, & t<2 \\ 0, & t \geq 2 \end{array}[/tex]

    I haven't looked closely at the rest of your equation, but you should fix this first and see if that does the trick.
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