Results 1 to 2 of 2

Math Help - d'Almberts Forumla Help

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    Istanbul
    Posts
    18

    Exclamation d'Almberts Forumla Help

    I have a question regarding the image below.

    Is this how you solve it.

    1) Identify if its parabolic/hyperbolic/elliptic etc
    2) Find the charatertics coordinates
    3) Using the Initial condition, find the charatertics cooridnates for them
    4) sketch the charatertics coodinates in terms of x and t?

    d'Almberts Forumla Help-untitled.png

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: d'Almberts Forumla Help

    Quote Originally Posted by princessmath View Post
    I have a question regarding the image below.

    Is this how you solve it.

    1) Identify if its parabolic/hyperbolic/elliptic etc
    2) Find the charatertics coordinates
    3) Using the Initial condition, find the charatertics cooridnates for them
    4) sketch the charatertics coodinates in terms of x and t?

    Click image for larger version. 

Name:	Untitled.png 
Views:	11 
Size:	51.9 KB 
ID:	25007

    Thank you
    d'Alembert's formula gives us a simple solution when the intial velocity is zero.

    u(x,t)=\frac{1}{2}\left(f(x-ct)+f(x+ct)\right)

    where

    f(x)

    is the intial condition. In you equation c=1 so this gives the solution

    u(x,t)=\frac{1}{2}\left(u(x-t,0)+u(x+t,0) \right)

    u(x,t)=\frac{1}{2}\left(\begin{cases}2(x-t)+2, \quad -1 \le x-t \le 0 \\ 2-(x-t), \quad 0 \le x-t \le 2 \\ 0, \quad x-t < -1 \text{ or } x-t > 2 \end{cases} \right) + \frac{1}{2}\left(\begin{cases}2(x+t)+2, \quad -1 \le x+t \le 0 \\ 2-(x+t), \quad 0 \le x+t \le 2 \\ 0, \quad x+t < -1 \text{ or } x+t > 2 \end{cases} \right)

    This probably is not the best notation LOL.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Reversing forumla
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 27th 2011, 07:02 PM
  2. Heron's forumla
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 2nd 2010, 08:37 PM
  3. Transpose forumla.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 7th 2009, 08:27 AM
  4. Sequence Forumla?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 1st 2008, 11:53 PM
  5. Compound Angle Forumla
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 4th 2007, 07:47 AM

Search Tags


/mathhelpforum @mathhelpforum