Period T & Length: Can the Term in Parentheses be Constant?

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The discussion centers on the relationship between the period T of a pendulum and its length l, as described by the formula T=2pi(sqrt l/g). It asserts that the term in parentheses cannot be treated as a constant of proportionality because while the acceleration due to gravity g remains constant, the length l varies. The concept of proportionality is clarified, emphasizing that two quantities are proportional only if one is a constant multiple of the other. The user mentions having graphs of T against amplitude, length, and mass, indicating a pendulum experiment. The challenge lies in effectively explaining the relationships illustrated in these graphs.
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Using Newton’s laws, we could show that for some pendulums, the period T is related to the length and free-fall acceleration g by


T=2pi(sqrt l/g)


Can the term in parentheses be treated as a constant of proportionality?
 
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No, because g is always the same, and l varies depending on the pendulum
 
mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.

I have graphs of T vs. A, T vs L, T vs m

A=Amplitude
L=Length
m=bob mass

It's a pendelum experiment
I have graphs but how would i explain it in the graph
 

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