Dimensional analysis of simple pendulm

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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 * m^al^bg^cs^d

[T]=m^al^bg^cs^d
=[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

 

[Brown Arrow]

a=0
b+c+d=0
-2c=1 => c=-1/2

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

T=l^1/4g^-1/2s^1/4

but T= 2π (l/g)^1/2

what i did is is correct?

 

[Brown Arrow]

could someone help me out here?