Results 1 to 5 of 5

Math Help - What is the inverse Laplace transormation of this please?

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    14

    What is the inverse Laplace transormation of this please?

    Hi I'm trying to work out the inverse Laplace transform of 4/[(s-2)^2 + 16]

    Could anyone help please? I have tried factorising the denominator part which can also be written as s^2 - 4s + 20 but aren't there only surd factors to satisfy this? I think I'm better leaving it in its original completed square form but I'm if I do I'm not sure how to go about doing the partial fractions stage to find a standard inverse transform...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2011
    From
    Belgium
    Posts
    36

    Re: What is the inverse Laplace transormation of this please?

    you have to split the denominator in (s-2-4i)(s-2+4i)

    -1/8 i e^{(2-4 i) t} (-1+e^{8 i t})
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,796
    Thanks
    1576

    Re: What is the inverse Laplace transormation of this please?

    Quote Originally Posted by chunkylumber111 View Post
    Hi I'm trying to work out the inverse Laplace transform of 4/[(s-2)^2 + 16]

    Could anyone help please? I have tried factorising the denominator part which can also be written as s^2 - 4s + 20 but aren't there only surd factors to satisfy this? I think I'm better leaving it in its original completed square form but I'm if I do I'm not sure how to go about doing the partial fractions stage to find a standard inverse transform...
    \displaystyle \begin{align*} \mathbf{L}^{-1}\left\{\frac{4}{(s-2)^2 + 16}\right\} &= e^{2t}\,\mathbf{L}^{-1}\left\{ \frac{4}{s^2 + 4^2} \right\} \\ &= e^{2t}\sin{\left(4t\right)} \end{align*}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2011
    Posts
    14

    Re: What is the inverse Laplace transormation of this please?

    Thanks Prove It, that's a great help. Is there an intermediate step you did to get e^2t L^-1 (4/s^2 + 4^2)?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,796
    Thanks
    1576

    Re: What is the inverse Laplace transormation of this please?

    Quote Originally Posted by chunkylumber111 View Post
    Thanks Prove It, that's a great help. Is there an intermediate step you did to get e^2t L^-1 (4/s^2 + 4^2)?
    It's the horizontal shifting theorem.

    \displaystyle \begin{align*} \mathbf{L}\left\{ e^{a\,t}f(t) \right\} = F(s - a) \end{align*} .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laplace/Inverse Laplace Questions
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 14th 2010, 12:29 PM
  2. Help with inverse laplace
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: July 15th 2010, 04:11 PM
  3. inverse laplace
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 16th 2010, 03:25 AM
  4. Inverse Laplace
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 16th 2009, 03:22 AM
  5. Inverse Laplace
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: June 1st 2009, 09:54 PM

Search Tags


/mathhelpforum @mathhelpforum