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Homework Help: Is this the correct approach? (finding frequency of oscillation)

  1. Feb 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the frequency of small oscillations around the minimum of the potential

    2. Relevant equations
    Force is the negative of the gradient of the potential...

    3. The attempt at a solution
    Given the problem statement bit, "around the minimum," I take this as a hint to find the taylor expansion of U(x) to approximate the potential at the minimum.

    In doing the taylor expansion at 0, I get that:
    U(x) ≈ x^2

    The force on a particle in this potential is given by:
    F = -dU/dx = -2x.

    And so we have that:
    F + 2x = 0 => mx'' + 2x = 0. Solving this differential equation, we have something of the form:
    x = A*cos(√(2/m)t - [itex]\phi[/itex])

    So, we have, the angular frequency to be: ω = √(2/m).

    Finally, the frequency is then: [itex]\nu[/itex] = ω/(2∏) = √(2/m)/(2∏) = (2m∏^2)^(-1/2)

    Does this seem correct? I was a little confused that the frequency is dependent on the mass, but then I see that the potential given is independent of mass. But thats a bit odd. Thanks.
  2. jcsd
  3. Feb 8, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    This all seems entirely correct to me.

    Your teach can come up with any kind of potential he wants! :smile:
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