How to Find the Laplace Transform of a Piecewise Continuous Function?

[sara_87]

Homework Statement

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)

Homework Equations

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

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 I am missing something.

Thank you.

 

[gabbagabbahey]

To start with, -tH(t-2)= \left\{ \begin{array}{lr} 0, &amp; t&lt;2 \\ -t, &amp; t \geq 2 \end{array} \neq \left\{ \begin{array}{lr} t, &amp; t&lt;2 \\ 0, &amp; t \geq 2 \end{array}I haven't looked closely at the rest of your equation, but you should fix this first and see if that does the trick.