Dimension Analysis Homework: Buckingham Theorem

[dirk_mec1]

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?

 

[dirk_mec1]

What I meant is that sin(phi) has the same dimension as phi so the answers of a and b are the same, right?

 

[DorianG]

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 )

 

[Redbelly98]

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

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.

 

[dirk_mec1]

Thanks for the confirmation redbelly.