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Differential equation

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data

    y'' + 24y' +432y = cos (wt)

    yp(x) = R(h) cos (ht - ∅(h))

    find R(h)
    and hbar = value for h which R(h) is max.
    and ∅(hbar)

    2. Relevant equations

    double angle formula for cos
    cos (a-b) = cos a cos b + sin a sin b

    3. The attempt at a solution

    solving the equation as a quadratic in coefficients on sin and cos, hbar = 12
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 4, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Frankly, I can't figure out what your question is. What is yp? Is it supposed to be a particular solution? If so, you will need to find yp' and yp'' and put them into the equation. What do you get when you do that?
     
  4. Feb 4, 2012 #3
    yes yp is the particular solution.

    Well i thought of using a trial particular solution of

    yp= A sin (Ht) + B cos (Ht)

    which leaves me with

    -AH2-24BH+432A = 0 for coefficients of sin(Ht)

    and

    -BH2+24AH+432B = 1 for coefficients of cos(Ht)
     
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