The Relationship Between Length and Frequency in a Simple Pendulum

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SUMMARY

The discussion centers on the frequency of a simple pendulum when its length is altered. Specifically, cutting a meter stick in half raises the frequency, but the participants debate the correct relationship. The consensus indicates that the frequency of a pendulum is inversely proportional to the square root of its length, contradicting the initial assumption that halving the length doubles the frequency. This misunderstanding highlights the need for clarity on pendulum motion equations.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with pendulum dynamics
  • Knowledge of frequency and its mathematical relationships
  • Basic grasp of oscillatory systems
NEXT STEPS
  • Study the formula for pendulum frequency: f = (1/2π) * √(g/L)
  • Explore the effects of length on oscillation frequency in pendulums
  • Investigate the differences between pendulums and tuning forks in terms of frequency
  • Review the principles of simple harmonic motion and its applications
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the principles of oscillatory motion and pendulum behavior.

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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