1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Laplace transform,partial fraction problem

  1. Aug 12, 2013 #1
    This is more of a pre calc question but it dose however come from diff eqs, just in case I have made fundamental mistakes, i have posted it here. I have been studying this topic for few days by myself, never had any problems with algebra until here.

    really appreciate all of your help.

    1. The problem statement, all variables and given/known data
    problem comes from here.
    [itex]y''-2y'-2y=0[/itex] with initial conditions [itex]y(0) = 2 , y'(0) = 0[/itex]

    I am stuck trying to decompose this line
    [itex]\mathcal Y(s) = (2s+4)/(s^2-2s-2)[/itex]

    2. Relevant equations
    Laplace Transforms Tables

    3. The attempt at a solution
    [itex]y''-2y'-2y=0[/itex]

    [itex]s^2\mathcal Y(s) - 2s - 2s\mathcal Y(s) -4 -2\mathcal Y(s) = 0[/itex]
    [itex](s^2-2s-2)\mathcal Y(s) -2s-4=0[/itex]
    [itex]\mathcal Y(s) = (2s+4)/(s^2-2s-2)[/itex]
    and stuck here.. I cant figure out how to decompose last line.
     
  2. jcsd
  3. Aug 12, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Complete the square in the denominator: ##(s-1)^2-3##. Then write the numerator as ##2(s-1)+6##. Does that help?
     
  4. Aug 12, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Are you required to use "Laplace Transform"? I have never quite understood why "Laplace Transform" methods are even taught for differential equations! Just writing out the characteristice equation for the given differential equation, [itex]r^2- 2r+ 2= r^2- 2r+ 1+ 1= 0[/itex] gives [itex]r= 1\pm i[/itex] as characteristic solution and so [itex]y(t)= e^{t}(C_1cos(t)+ C_2 sin(t))[/itex] as general solution to the differential equation.
     
  5. Aug 12, 2013 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That's ##r^2 -2r -2##, which changes the answer a bit. While I somewhat agree with your sentiments, the transforms are certainly handy for non-homogeneous terms which are piecewise defined, not to mention the usefulness of the transform space in EE applications.
     
  6. Aug 12, 2013 #5
    I dont see how this came about. can you elaborate?
     
  7. Aug 12, 2013 #6
    we spent last semester doing just that, I am only studying ahead so I have yet to find out why myself. i have heard it is important for EE students, which is what I am.
     
  8. Aug 12, 2013 #7

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Are you asking how to complete the square in a quadratic? If so, look in any algebra book or look here:

    http://en.wikipedia.org/wiki/Completing_the_square

    For the second one, just expand it out to see it's the same.
     
  9. Aug 12, 2013 #8
    thank you for that, this topic opened a can of loop holes in my algebra! really appreciate your help. understand it now!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Laplace transform,partial fraction problem
Loading...