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Second order linear differential equations

  1. Apr 6, 2010 #1
    1. The problem statement, all variables and given/known data
    a) ẍ + 5ẋ + 4x = 0
    x(0) = 0, ẋ(0)=1
    What type of damping?

    b) ẍ + x = cos(t)
    x(0) = 0, ẋ(0)= 1
    What type of motion?

    3. The attempt at a solution
    a) Let x = R Eᴿᵀ

    R = -4
    R = -1

    x(t) = CE**-4T + DE**-t

    C + D = 0
    -4C - D = 1

    C = 1/5
    D = 1/5

    And it is over damping

    I think this is the right answer for a) but i have no idea how to do b)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 6, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    a is correct, didn't check your values though.

    You need to solve b) in the same way.

    Set the LHS to zero and solve for xh

    and your steady-state solution would be the PI for the right side.
     
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