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Dimensional analysis

  1. Nov 22, 2007 #1
    1. A simple pendulum consists of a light inextensible string AB with length L, with the end A fixed, and a perticle of mass M attatched to B. The pendulum oscillates with period T.

    It is suggested that T is proportional to the product of powers of M, L and g. Use dimensional analysis to find this relationship.

    2. T = K (l/g)1/2

    3. ?? Dont know where to start on this one. some sort of substitution to find the variables, but i dont know how.
  2. jcsd
  3. Nov 22, 2007 #2
    also, i am presuming that little g is the surface gravity, ie, 9.81. I think thats what that represents, but i better check that out first.
  4. Nov 22, 2007 #3

    Doc Al

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    Staff: Mentor

    Yes, g stands for the acceleration due to gravity. What are its dimension?
  5. Nov 22, 2007 #4
    g is in N/Kg i think? is that what you mean by its dimension?
  6. Nov 22, 2007 #5

    Doc Al

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    Staff: Mentor

    Those are units. By dimensions I mean something independent of particular units. The fundamental dimensions are length (L), mass (M), and time (T). So, how would you express the dimension of g in terms of these quantities?

    Here's a wiki page that might help you: Dimensional analysis
  7. Nov 22, 2007 #6
    Yep, sure did help, they pretty much has this exact question as an example on that page;

    so, i basically substitiute dimensions, equate indices and solve.

    T = kma Lb gc => T = Ma Lb (LT-2)c

    a = 0

    -2c = 1 => c = 0.5

    b + c = 0 => b = 0.5,

    ...so T = K (L/G)1/2

    I think thats right, cheers. :smile:
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