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=2π(sqrt(l/g)), where g represents free-fall acceleration. It is established that the term in parentheses cannot be treated as a constant of proportionality due to the variability of length l while g remains constant. The user also mentions having graphs depicting the relationships between T and amplitude A, T and length L, and T and bob mass m, indicating a pendulum experiment aimed at visualizing these relationships.

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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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