Dimensional analysis of simple pendulm

AI Thread Summary
The discussion focuses on using dimensional analysis to determine the relationship between the period T of a simple pendulum and its variables: mass m, weight w, length l, and arc-length s. The user expresses confusion about including arc-length in their analysis and seeks clarification. After some calculations, they derive an equation for T but question its correctness compared to the known formula T = 2π (l/g)^(1/2). The user concludes by asking for validation of their approach and results. Overall, the thread highlights the challenges of applying dimensional analysis in physics problems.
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Homework Statement



Use dimensional analysis to determine the dependence of the period T of
a simple pendulum on its mass m , weight w , length l and arc-length of
swing s.

Homework Equations


g= [L/T2]

The Attempt at a Solution



T =cst * malbgcsd

[T]=malbgcsd
=[M]a[L]b[g]c[L]d
okay I am making a mistake here aren't I? by including the arc-Length? i do not know why i should not include it? some one explain? I am a bit confused... after this I'll be able to go on.

then i will equate the exponents and solve it.

EDIT: Thanks in advance
 
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a=0
b+c+d=0
-2c=1 => c=-1/2

b+d=1/2 ==> b=d=1/4

T=l1/4g-1/2s1/4

but T= 2π (l/g)1/2

what i did is is correct?
 
could someone help me out here?
 

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