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Spring problem

  1. Aug 29, 2007 #1
    1. The problem statement, all variables and given/known data and 2. Relevant equations

    Find position/velocity of a mass m attached to a spring of constant k when subjected to an oscillatinf roce

    [tex]
    F(t) = F sin(Bt)
    [/tex]

    With [tex]B\not = \sqrt{k/m}[/tex]

    3. The attempt at a solution

    Model;

    [tex]
    mx'' + kx = F \sin(Bt)
    [/tex]

    I have no idea if/how it can be solved (without a computer, of course). Because;

    [tex]
    mr^2 + k = 0
    [/tex]

    Gives

    [tex]
    r = ±\sqrt{-k/m}
    [/tex]

    As [tex]B\not = \sqrt{k/m}[/tex] it can't be an answer.
     
  2. jcsd
  3. Aug 29, 2007 #2

    Astronuc

    User Avatar

    Staff: Mentor

  4. Aug 30, 2007 #3
    I'm not sure I understand your point, it's more a problem of math than a problem of physics, I must solve;

    [tex]
    mx'' + kx = F \sin(Bt)
    [/tex]

    But I don't know how
     
  5. Aug 30, 2007 #4

    learningphysics

    User Avatar
    Homework Helper

    First solve the homogenous equation first:

    mx'' + kx = 0

    Then you need a particular solution for
    [tex]
    mx'' + kx = F \sin(Bt)
    [/tex]

    just plug in x = Asin(Bt) into the differential equation and solve for A...

    Then your general solution is the solution for the homogenous equation + the particular solution Asin(Bt)...

    And finally you need to deal with initial conditions...
     
  6. Aug 30, 2007 #5
    Thx for the help, I solved the diff. equation. But will the solution to the differential equation give me the position or the velocity at time t ? And there's no initial condition, only [tex]B\not = \sqrt{k/m}[/tex], I don't know what to do with it.
     
  7. Aug 30, 2007 #6
    You actually need two boundary conditions, but since you don't have them you can probably just leave the two constants unsolved for.
     
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