Results 1 to 2 of 2

Math Help - Piecewise initial value Laplace

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    65

    Piecewise initial value Laplace

    Here is the question:

    y'' + 64y = {P

    P =
    2t, 0<=t<2
    0, t>=2

    y'(0) = 0
    y(0) = 0

    Find the equation you get by taking the Laplace transform of the differential equation and solve for

    Y(s) = ?

    Please help!!

    I tried and got this as answer but it's wrong...

    2/(s^2(s^2+64))
    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
    An alternative expression for p(t) is...

    p(t)= 2t\cdot \{1-\mathcal{U} (t-2)\} (1)

    ... and the DE in terms of LT is...

    s^{2}\cdot Y(s) + 64\cdot Y(s) = P(s) (2)

    ... where Y(s) = \mathcal{L}\{y(t)\} and P(s) = \mathcal{L}\{p(t)\}, so that is...

    Y(s)= \frac{P(s)}{s^{2} +64} (3)

    What is P(s), i.e.the LT of (1)?...

    Kind regards

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

Similar Math Help Forum Discussions

  1. Laplace Transform of a Continuous Piecewise Function
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 28th 2010, 04:27 PM
  2. Piecewise Laplace 3
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 5th 2009, 09:35 AM
  3. Piecewise Laplace 1
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 2nd 2009, 06:41 PM
  4. Piecewise Laplace 2
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 30th 2009, 04:36 PM
  5. Piecewise laplace transformation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 22nd 2009, 09:33 PM

Search Tags


/mathhelpforum @mathhelpforum