Dimension Analysis Homework: Buckingham Theorem

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Homework Help Overview

The discussion revolves around the application of the Buckingham theorem in the context of dimensional analysis, specifically comparing two equations involving the sine function and an angle phi in a pendulum scenario.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the sine of an angle and the angle itself, questioning whether the differences in the equations are significant. They discuss the implications of small-angle approximations and the dimensionality of the variables involved.

Discussion Status

Some participants have provided insights into the nuances of the sine function's behavior at small angles, while others have confirmed the perceived lack of essential difference between the two equations. The conversation reflects a mix of interpretations regarding the dimensional analysis and the assumptions made in the problem.

Contextual Notes

There is mention of the problem statement indicating that phi is small for part b, which may influence the dimensional analysis being discussed. Participants are considering how this affects the equations in question.

dirk_mec1
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Homework Statement



http://img21.imageshack.us/img21/613/70858934fn5.png

Homework Equations


Buckingham theorem

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?
 
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What I meant is that sin(phi) has the same dimension as phi so the answers of a and b are the same, right?
 
sin(phi) is only equivalent 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 )
 
Last edited by a moderator:
It says in the problem statement that phi is small for part b. The question is about expressing the equations in dimensionless variables.

dirk_mec1 said:
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?

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.
 
Thanks for the confirmation redbelly.
 

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