Results 1 to 3 of 3

Math Help - Inverse Laplace Transforn

  1. #1
    Newbie
    Joined
    Sep 2006
    Posts
    7

    Question Inverse Laplace Transforn

    Hello!
    Could anyone help me solve the problem below? I've tried it all day but I have stuck. Thanks a lot!

    Problem
    Find the inverse Laplace transform of {(e^(-a/s))/Sqrt[s]}, a>0, knowing that InverseLaplaceTransform{(e^(-1/s))/Sqrt[s]} = (cos(2Sqrt[t]))/Sqrt[Pi*t]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by jmytil View Post
    Hello!
    Could anyone help me solve the problem below? I've tried it all day but I have stuck. Thanks a lot!

    Problem
    Find the inverse Laplace transform of {(e^(-a/s))/Sqrt[s]}, a>0, knowing that InverseLaplaceTransform{(e^(-1/s))/Sqrt[s]} = (cos(2Sqrt[t]))/Sqrt[Pi*t]
    You have:

    L {cos(2 sqrt(t))/sqrt(pi t)} = exp(-1/s)/sqrt(s) ... (1)

    Now we also know that:

    L uF(ut) = f(s/u) ... (2)

    Now let u=a and use (2) in (1):

    L {a cos(2 sqrt(at))/sqrt(pi at)} = exp(-a/s)/sqrt(s/a)
    ............................................= sqrt(a) exp(-a/s)/sqrt(s).

    Hence:

    L {sqrt(a) cos(2 sqrt(at))/sqrt(pi at)} = exp(-a/s)/sqrt(s).

    So the inverse LT of exp(-a/s)/sqrt(s) is sqrt(a) cos(2 sqrt(at))/sqrt(pi at).

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2006
    Posts
    7

    Smile

    Quote Originally Posted by CaptainBlack View Post
    You have:

    L {cos(2 sqrt(t))/sqrt(pi t)} = exp(-1/s)/sqrt(s) ... (1)

    Now we also know that:

    L uF(ut) = f(s/u) ... (2)

    Now let u=a and use (2) in (1):

    L {a cos(2 sqrt(at))/sqrt(pi at)} = exp(-a/s)/sqrt(s/a)
    ............................................= sqrt(a) exp(-a/s)/sqrt(s).

    Hence:

    L {sqrt(a) cos(2 sqrt(at))/sqrt(pi at)} = exp(-a/s)/sqrt(s).

    So the inverse LT of exp(-a/s)/sqrt(s) is sqrt(a) cos(2 sqrt(at))/sqrt(pi at).

    RonL


    THANK YOU VERY MUCH!!!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laplace Inverse
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2011, 04:50 PM
  2. Laplace/Inverse Laplace Questions
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 14th 2010, 11:29 AM
  3. Inverse Laplace
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 16th 2009, 02:22 AM
  4. Inverse Laplace
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: June 1st 2009, 08:54 PM
  5. Replies: 0
    Last Post: November 28th 2008, 11:25 PM

Search Tags


/mathhelpforum @mathhelpforum