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Finding the frequency of a vibrating particle on a string?

  1. Jan 14, 2016 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m is on a massless string of length 3a, which is held horizontally across with a tension T(which you can assume doesn't change with the small vibrations). The particle is a distance of a from one of the edges. Set up a diff. equation that describes the particles motion with time and find its frequency of oscillations.

    2. Relevant equations
    mx'' = net force
    x''+(ω^2)x=0 => x=Acos(ωt+φ)
    3. The attempt at a solution
    I originally wrote mx'' = T - mg but this doesn't work since it doesn't involve x and doesn't account for the changing sign of T depending if that particle is above or below the equilibrium point. I tried to describe its position but the best I could do was x(θ) = arctan(x/a) and not x(t) which is what I want (at least I think because then I could take the derivative twice and get the acceleration). Any tips would be appreciated!
     
  2. jcsd
  3. Jan 14, 2016 #2

    Simon Bridge

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    Welcome to PF;
    Presumably the particle is displaced and then released or something?
    You need to start by drawing a diagram of the string and mass when the mass has some arbitrary displacement from it's equilibrium.
    Then draw the free body diagram for the mass - notice that T points along the string.
    Try to reserve bold-face for vectors only.
     
  4. Jan 14, 2016 #3
    That would make more sense... I was only thinking of the component of T parallel to the particles displacement. Thanks!
     
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