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Homework Help: Dimension analysis

  1. Feb 4, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img21.imageshack.us/img21/613/70858934fn5.png [Broken]

    2. Relevant equations
    Buckingham theorem

    3. The attempt at a solution
    My question is what is the difference between question a and b? The sine doesn't influence the dimension. Or is it a question to trick me?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 5, 2009 #2
    What I meant is that sin(phi) has the same dimension as phi so the answers of a and b are the same, right?
  4. Feb 5, 2009 #3
    sin(phi) is only equivelent to phi (approximately) for very small phi, i.e. very small oscillations of the pendulum, when simple harmonic motion occurs.
    Above very small angles, formula (a) is correct, (b) incorrect, as the variation between phi and sin(phi) becomes significant.
    Look at Small-angle Approximation on the following link:
    http://en.wikipedia.org/wiki/Pendulum_(mathematics [Broken])
    Last edited by a moderator: May 4, 2017
  5. Feb 5, 2009 #4


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    It says in the problem statement that phi is small for part b. The question is about expressing the equations in dimensionless variables.

    I think the question really is as easy as it seems: no essential difference between the two equations, other than replacing φ with sin(φ). Once you've converted one equation to a dimensionless form, you basically have the other.
  6. Feb 5, 2009 #5
    Thanks for the confirmation redbelly.
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