The Relationship Between Length and Frequency in a Simple Pendulum

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Cutting the bottom half of a meter stick pendulum affects its frequency, but the relationship is not as straightforward as doubling the frequency. The frequency of a simple pendulum is determined by its length, with the formula f = (1/2π)√(g/L), where g is the acceleration due to gravity and L is the length of the pendulum. When the length is halved, the frequency increases, but not necessarily to twice the original frequency; it actually increases by a factor of √2. The confusion arises from comparing the pendulum's behavior to that of a tuning fork, which operates under different principles. Understanding the correct equations for pendulum motion is crucial for accurately determining frequency changes.
marine192
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A meter stick swinging from one end oscillates with a frequency f0. What would be the frequency, in terms of f0 , if the bottom half of the stick were cut off?







Based on a experiment we did in class with tuning forks the frequency should be twice as much if the length were reduced by half but when I enter that in for the answer it comes up as incorrect. Today in class we went over that a frequency remains the same when transferring between mediums but there is no transfer here, just a shortening of length so that shouldn't have any effect on it. I can't figure out where I am going wrong with this.
 
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welcome to pf!

hi marine192! welcome to pf! :smile:

a pendulum isn't remotely like a tuning fork

(btw, http://en.wikipedia.org/wiki/Tuning_fork#Calculation_of_frequency" says frequency of a tuning fork is inversely proportional to length squared, but there's no reference for it :frown:)

do you know any equations that may help to describe the motion of a pendulum?
 
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