Results 1 to 2 of 2

Math Help - laplace help

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    29

    laplace help

    f (t) = {1 0 < t < a
    {0 a < t < 2a


    If f(t + 2a) = f(t), t>0
    f(t) is called: _______________


    and its graph for 0 < t < 4a looks like:




    and

    L{f(t)} = ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    If You have a function defined as...

    \sigma(t)=\left\{\begin{array}{cc}1,&\mbox{ if }<br />
0<t<a\\0, & \mbox{ if } t>a\end{array}\right. (1)

    ... then is...

    \mathcal{L}\{\sigma(t)\} = \frac{1-e^{-as}}{s} (2)

    Now if f(t) is \sigma(t) 'periodically extended' with period 2a is...

    \mathcal{L}\{f(t)\} = \frac{\mathcal{L}\{\sigma(t)\}}{1-e^{-2as}}= \frac{1-e^{-as}}{s\cdot (1-e^{-2as})} (3)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. laplace
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: May 10th 2011, 01:34 PM
  2. PDE by Laplace
    Posted in the Differential Equations Forum
    Replies: 24
    Last Post: September 2nd 2010, 03:35 PM
  3. Laplace/Inverse Laplace Questions
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 14th 2010, 11:29 AM
  4. laplace help
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: August 13th 2010, 05:19 AM
  5. laplace eqn help
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: August 12th 2008, 12:21 AM

Search Tags


/mathhelpforum @mathhelpforum