Relationship between Period of a pendulum and length

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Homework Help Overview

The discussion revolves around the relationship between the period of a pendulum and its length, specifically examining the formula t=2π√(L/g). Participants are exploring the underlying principles and assumptions that connect these variables.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand how the formula is derived and why it includes the factor of 2π. They express uncertainty about the relationship and mention an attempt to graph the period against length, which resulted in a curve.

Discussion Status

Some participants have offered hints regarding the equation for simple harmonic motion and the small angle approximation, suggesting avenues for further exploration without providing direct solutions. The discussion appears to be open-ended with multiple lines of inquiry being considered.

Contextual Notes

The original poster indicates a lack of understanding of the formula's derivation and its components, which may suggest constraints in their background knowledge or the complexity of the topic being discussed.

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Homework Statement



The formula to find the period of a pendulum is t=2pi √ L/g
where pi = 3.14...
L=length of pendulum
g=gravity

So I was wondering how all of this was put together. How they related together? Why it is multiplied by 2pi

The Attempt at a Solution


I really don't know, it's I'm asking here. I tried graphing it and it gives me a curve.
 
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Hint: Write the equation for simple harmonic motion in terms of [itex]\theta[/itex]
 
And use a small angle approximation. That is:

[tex]sin \theta ~= \theta[/tex]

This is applied when an angle is pretty small.
 
thank you!
 

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