How do you calculate gravitational acceleration with a pendulum?

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Discussion Overview

The discussion revolves around calculating gravitational acceleration ('g') using a pendulum's length and period, specifically through the equation T = 2π√(L/g). Participants explore how to prove this equation and the implications of its approximations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant seeks clarification on how to prove the equation T = 2π√(L/g) and expresses curiosity about its derivation.
  • Another participant suggests approximating the pendulum as a mass-spring system, noting that the restoring force is not perfectly linear but approaches linearity for small angles.
  • Some participants emphasize that the equation is an approximation, particularly valid for small swing amplitudes.
  • A participant questions whether there exists a non-approximate equation for the period of a pendulum and discusses the independence of the period from the mass and release angle, assuming no air resistance or friction.
  • There is a reference to Galileo's claims regarding pendulum periods being independent of the arc size, which some participants challenge based on their understanding of the physics involved.
  • One participant expresses confusion about the relationship between initial angle and period, indicating a need for clarification on the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the approximation for the period of a pendulum, with some arguing that it is dependent on the amplitude while others reference historical claims suggesting independence from the arc size. The discussion remains unresolved regarding the existence of a non-approximate equation.

Contextual Notes

Participants mention limitations related to the assumptions of small angles and the effects of air resistance and friction, which are not fully resolved in the discussion.

Who May Find This Useful

This discussion may be useful for high school physics students studying pendulum motion, simple harmonic motion, and the derivation of related equations.

roobs
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How do you calculate 'g' when the length and the period is known for a pendulum
I know you do it by rearranging this equation T = 2π√(L/g).

But how exactly do you prove that equation??

just curious...:rolleyes:
 
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I don't know what your teacher wants but
the way that I would do it is to approximate the pendulum with a mass spring system.
The equations for a mass spring system are pretty easy.

You should be aware though that a pendulum doesn't perfectly resonate.
The restoring force isn't perfectly linear.
But for very small angles it approaches quite closely to it.

http://en.wikipedia.org/wiki/Simple_harmonic_motion#Mass_on_a_simple_pendulum

Simple_Pendulum_Oscillator.gif

Muelle.gif
 
Last edited by a moderator:
I know... but i am asking how we can prove this T = 2π√(L/g)
 
roobs said:
I know... but i am asking how we can prove this T = 2π√(L/g)

What have you tried and where are you stuck?
 
I answered your question and
I also pointed out that
your equation is only an approximation
 
Dadface said:
What have you tried and where are you stuck?

ermm...i do not know where to start yet

just tell me in words what that equation mean and how to prove it, no need for working out

Thanks
 
roobs said:
ermm...i do not know where to start yet

just tell me in words what that equation mean and how to prove it, no need for working out

Thanks

As granpa pointed out the equation is an approximation only but it works well provided that the amplitude of swing is small.The equation relates the time period(T) which is the time taken for one complete swing of the pendulum to the length(L) of the pendulum.g is the acceleration due to Earth's gravity.
 
how old are you
what class is this for

how much do you know about simple harmonic motion?
Have you done simple mass/spring systems yet?
You should do those before you try to do pendulums.
 
  • #10
okay... then is there an equation that is not an approximation??
Also, is it safe to say that the mass of the pendulum and the angle at which it is released does not change the period (assuming no air resistance and friction)?

I am a high school physics student and i have done mass/spring systems
 
  • #12
wow...okay...you are saying the value of T is different with a small initial angle and a large initial angle
but some sites say the period is not dependent on the initial amplitude, such as this one

http://muse.tau.ac.il/museum/galileo/pendulum.html

which stated " Galileo examined a variety of pendulums and claimed that the period of each is totally independent of the size of the arc through which it passes. A pendulum with an angle of 80 degrees has an identical period to that of a pendulum with an angle of 2 degrees."
 
  • #13
oops...i did not read the next part which said why galileo claims were wrong
okay i get most of this now
thanks a lot for the replies
 

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