Results 1 to 2 of 2

Math Help - Help with Method of Separation of Variables

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    13

    Help with Method of Separation of Variables

    I need help with the following questions:

    1.

    The differential equation governing the displacement of a stretched string is [see attached equation].

    Find the displacement of the string at any subsequent time t if the string is initially displaced as illustrated below and if it starts from rest.

    [See attached graph]

    Any help is most appreciated.
    Attached Thumbnails Attached Thumbnails Help with Method of Separation of Variables-equation.png   Help with Method of Separation of Variables-graph.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    You fail to mention how much the string is initially displaced by at (x,t) = \left( \frac{L}{2} , 0 \right). So let us call that value M.

    The partial differencial equation is the 1d wave equation:
    \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial u^2}{\partial x^2}.

    The initial value problem is:
    \left\{ \begin{array}{c}u(x,0) = f(x) \\ u_t(x,0) = 0 \end{array}\right. \mbox{ for }0<x<L.

    Where f(x) is the function described in your curve, which is,
    f(x) = \left\{ \begin{array}{c} \frac{2M}{L}x \mbox{ for }0 < x \leq \frac{L}{2} \\ \frac{2M}{L}\left( L - x \right) \mbox{ for }\frac{L}{2} \leq x < L \end{array} \right..

    And the boundary value problem is:
    u(0,t) = u(L,t) = 0 \mbox{ for }t\geq 0.

    See if you can solve this wave equation from heir.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Separation of Variables
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: January 5th 2011, 03:12 PM
  2. Separation of Variables
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: January 3rd 2010, 05:25 PM
  3. Separation of Variables
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: June 29th 2009, 06:49 PM
  4. separation of variables
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 9th 2008, 09:34 AM
  5. Separation of Variables
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 11th 2007, 04:17 AM

Search Tags


/mathhelpforum @mathhelpforum