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Determine an expression for the period of motion.

  1. Dec 3, 2011 #1
    problem solved, thanks
     
    Last edited: Dec 3, 2011
  2. jcsd
  3. Dec 3, 2011 #2

    Doc Al

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    I'm not understanding the problem. You have the equation you need, just change r to x. What would k be?

    The real question is: Can you solve it to find the period? (Compare it to the equations for simple harmonic motion.)

    FYI: Writing your equations using Latex will make things easier:
    [tex]F = - \frac{4G\pi\rho m}{3} r [/tex]
     
    Last edited: Dec 3, 2011
  4. Dec 3, 2011 #3
    k is the force constant.
     
  5. Dec 3, 2011 #4

    Doc Al

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    Sure, so in your equation what would it be?
     
  6. Dec 3, 2011 #5
    k = mω^2

    We haven't been given the values for anything, we're supposed to find the expression in a format of algerbra only.
     
  7. Dec 3, 2011 #6

    Doc Al

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    That's the solution for the usual simple harmonic motion equation. Since your equation (for gravity) has the same form, it will have the same solution. Compare the two equations you wrote before: What will take the place of 'k' in your equation?
    Right.
     
  8. Dec 3, 2011 #7
    Do you mean F = -kx

    and

    k = mω^2

    Therefore

    F = -mw^2 x
     
  9. Dec 3, 2011 #8

    Doc Al

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    I mean to take that equation and compare it to the one you wrote for your gravity problem. What would be the equivalent to k?
     
  10. Dec 3, 2011 #9
    OK give me a few minutes. I'm not very quite when it comes to rearranging and combing equations.
     
  11. Dec 3, 2011 #10

    Doc Al

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    You shouldn't have to rearrange anything, just read it off.

    Your equation has the form: Force = (some constant) x, what's that constant? (It's much easier than you think!)
     
  12. Dec 3, 2011 #11
    I'm over-complcating things then?

    I've just got to pop out anyway, so I'll have a think about it.
     
  13. Dec 3, 2011 #12

    Doc Al

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    I'd say so. You know the solution for the standard SHM problem of a mass on a spring. So you want to compare the equations, since the same equations have the same solutions.
     
  14. Dec 3, 2011 #13
    Not sure if my thinking is correct.

    k = 4Gπρ/3
     
  15. Dec 3, 2011 #14

    Doc Al

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    Almost! (You left out the mass.) But that's exactly the right idea.
     
  16. Dec 3, 2011 #15
    Oh yes, mass sorry, so,

    k = 4Gπρm/3

    Ok, i'm with you up to hear, just unsure how this applies to period of motion, which is what the question asks for.
     
  17. Dec 3, 2011 #16

    Doc Al

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    Well, what's the period for the standard SHM equation? (In terms of k.)
     
  18. Dec 3, 2011 #17
    You mean the frequency? ω?
     
  19. Dec 3, 2011 #18

    Doc Al

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    Well, you want the period. But you can express the period in terms of the frequency.
     
  20. Dec 3, 2011 #19
    Oh I see, the period, t.

    So, since ω = 2π/t

    t =2π/ω (is this correct? as i say, i'm terrible as rearranging equations)

    Not sure where to go from here.
     
  21. Dec 3, 2011 #20

    Doc Al

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    Good.

    Now use the expression for ω.
     
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