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Second order differential equation

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data
    if given the general solution to a differential equation
    y(t)=a cos t + b sin t + ((cos wt)/1-w^2),
    Find out how long it takes the solution to approach the steady state solution.
    original second order differential equation:
    y'' + y = cos wt such that 0 < w < 10

    2. Relevant equations



    3. The attempt at a solution
    I am not sure where to begin.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 11, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    So for y'' + y = cos wt

    What is your homogeneous solution?

    EDIT: Remember that your general solution will be y=yh+yss.
     
    Last edited: Apr 11, 2010
  4. Apr 11, 2010 #3

    Mark44

    Staff: Mentor

    The good news is that you are being very diligent in your use of parentheses, but the bad news is that some of them aren't in the right place. You should write the last expression above as cos(wt)/(1 - w^2). As you have it, this expression would be read as cos(wt)/1 - (w^2), or cos(wt) - w^2, and I'm pretty sure that's not what you intended.
    A good start would be to find out what the term "steady state solution" means.
     
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