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Mechanics problem about simple harmonic motion

  1. Aug 29, 2010 #1
    Hi,
    Can anyone help me with this question?


    The potential energy of mass (m=6KG) that is connected to a spring is given by:
    U(x) = 5x ^ 2 -10x +12

    Find the period of the small fluctuations around the equilibrium point (in seconds).
     
  2. jcsd
  3. Aug 29, 2010 #2

    Doc Al

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    Staff: Mentor

    What's the spring constant? Hint: How do you find the force as a function of x?
     
  4. Aug 29, 2010 #3
    Well, I guess F=10x-10

    and i've thought about doing

    10x-10=-kx
    but i don't think it will suffice.

    Doesn't there has to be some differential equation involved? I'm really scared of those...
     
  5. Aug 29, 2010 #4

    Doc Al

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    Staff: Mentor

    Almost. F = - dU/dx. (You just forgot the minus sign.)

    The constant just tells you that the equilibrium position is not at x = 0. You can read off the spring constant from that force equation.
    Sure, but it's the same differential equation as for any simple harmonic motion. I assume you know the solution by heart or can look it up. If you knew the spring constant and the mass, could you find the period?
     
  6. Aug 29, 2010 #5
    Unfortunately, you assume wrong :uhh:

    Perhaps someone can show me the mathematical steps needed to solve this?
     
  7. Aug 29, 2010 #6

    Doc Al

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    Staff: Mentor

    http://en.wikipedia.org/wiki/Simple_harmonic_motion" [Broken]
     
    Last edited by a moderator: May 4, 2017
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