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Forced oscillation

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Please help me solve this differential equation: This is mass attached to a spring, we have

    F= ma= -kx -bv + Fext where k and v are spring constant and velocity respectively and Fext is an additional external force.


    2. Relevant equations
    I know how to solve nonhomogeneous differential equations mathematically but on the right of the above equation is not a function so I stuck.

    3. The attempt at a solution

    I tried this way:
    writing the above as differential equation I have
    md2x/dt2 + bdx/dt + kx = Fext
    for homogeneous part md2x/dt2 + bdx/dt + kx=0
    the solution I assumed is x(t) =Aept
    the first derivative of the assumed solution is x'(t)= Apept and the second derivative is x''(t)= Ap2ept
    substituting all these x(t), x'(t) and x''(t) to the differential equation and devide by
    Aept I get:

    mp2 + bp+k=0
    for inhomogeneous part I don't know ho to handle this right hand side Fext. Please help me.
     
    Last edited: Mar 17, 2012
  2. jcsd
  3. Mar 17, 2012 #2

    tiny-tim

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    Hi Lizwi! :smile:
    Is Fext a constant?

    You need to find any solution for the whole equation …

    try polynomials first (starting with constants!) :wink:
     
  4. Mar 18, 2012 #3

    rude man

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    You need to know the explicit expression for your driving function first, so you can "guess" at the inhomogeneous solution. What is it?
     
  5. Mar 18, 2012 #4

    OldEngr63

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    You could express the solution for any right side function by means of a convolution integral, but that is only a symbolic solution and not good for too much.
     
  6. Mar 18, 2012 #5
    just absorb the external force into x i.e. x' = x + F. If it's a constant then it's not too difficult to solve, if it isn't then you have another (manageable) diff equation to solve.
     
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