1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Laplace Transform

  1. Mar 10, 2009 #1

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    From the class notes:
    [tex]\begin{array}{l}
    y'' + 8y' + 16y = te^{ - 4t} ,\,\,\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 0 \\
    \\
    L\left[ {y''} \right] + 8L\left[ {y'} \right] + 16L\left[ y \right] = \frac{1}{{\left( {s + 4} \right)^2 }} \\
    \end{array}[/tex]

    How did he get [tex]\frac{1}{{\left( {s + 4} \right)^2 }}[/tex] ?
    From the table, [tex]t = \frac{1}{{s^2 }}[/tex] and [tex]e^{at} \to \frac{1}{{s - a}}[/tex]
    How do these combine to give [tex]\frac{1}{{\left( {s + 4} \right)^2 }}[/tex] ?

    The next line is
    [tex]s^2 y\left( s \right) - sy\left( 0 \right) - y'\left( 0 \right) + 8\left( {sy\left( s \right) - y\left( 0 \right) + 16y\left( s \right)} \right) = \frac{1}{{\left( {s + 4} \right)^2 }}[/tex]

    Where did everything on the left side of = come from? The table doesn’t have y’’ or y’.

    After this, the problem looks like it turns into algebra.
     
  2. jcsd
  3. Mar 10, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    Hi Tony

    The laplace transform of a product is not just the Laplace transform of the components, have a look at this table:
    http://www.efunda.com/math/laplace_transform/forward.cfm?FuncName=Basic
    shows:
    [tex]L(e^{-\alpha t}) = \frac{1}{{\left( {s + 4} \right)^2 }}[/tex]
    to get the relation you actually need to perform the integral


    the next line comes about from the Laplace transform rules for derivatives, see this table
    http://www.vibrationdata.com/Laplace.htm
    these can be derived using integration by parts on successive derivatives if i remember rightly...
     
  4. Mar 10, 2009 #3

    tony873004

    User Avatar
    Science Advisor
    Gold Member

    Thanks. The 6th entry in the 1st table you linked to has the right side of my equation. It was missing from the table I had from class notes. And thanks for the 2nd table. I think it explains it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Laplace Transform
  1. Laplace Transformation (Replies: 5)

  2. Laplace Transform (Replies: 1)

  3. Laplace Transforms (Replies: 4)

  4. Laplace transformation (Replies: 2)

  5. Laplace transform (Replies: 3)

Loading...