Relationship between Period of a pendulum and length

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SUMMARY

The period of a pendulum is determined by the formula t = 2π √(L/g), where L represents the length of the pendulum and g is the acceleration due to gravity. The multiplication by 2π arises from the relationship between circular motion and harmonic motion. For small angles, the approximation sin(θ) ≈ θ simplifies the analysis of the pendulum's motion. Understanding these relationships is crucial for solving problems related to simple harmonic motion.

PREREQUISITES
  • Understanding of basic trigonometry and the sine function
  • Familiarity with the concepts of simple harmonic motion
  • Knowledge of gravitational acceleration (g = 9.81 m/s²)
  • Ability to manipulate algebraic equations and perform graphing
NEXT STEPS
  • Study the derivation of the formula for the period of a pendulum
  • Explore the concept of simple harmonic motion in greater detail
  • Learn about the small angle approximation and its applications
  • Investigate the effects of varying pendulum length on period
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in the principles of pendulum motion and harmonic oscillators.

Dynamite
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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 \theta
 
And use a small angle approximation. That is:

sin \theta ~= \theta

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

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