Understanding Pendulum Frequency & Period Changes

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SUMMARY

Shortening a pendulum directly affects its frequency and period. When the length of the pendulum decreases, its frequency increases, leading to a shorter period for each complete swing. This relationship is mathematically defined by the formula for the period of a simple pendulum, T = 2π√(L/g), where L is the length and g is the acceleration due to gravity. Thus, a shorter pendulum results in a faster oscillation and reduced time for each cycle.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with the formula for pendulum period (T = 2π√(L/g))
  • Basic knowledge of frequency and period relationships
  • Concept of gravitational acceleration (g)
NEXT STEPS
  • Study the mathematical derivation of the pendulum period formula
  • Explore the effects of varying gravitational acceleration on pendulum motion
  • Investigate the impact of mass on pendulum frequency
  • Learn about damped and driven pendulum systems
USEFUL FOR

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

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Homework Statement



If a pendulum is shortened, does its frequency increase or decrease? What about its period?

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The Attempt at a Solution


I think that the frequency will increase because the length of the string will now be shorter. As far as the period I think it will decrease because the pendulum should swing faster so the time for one cycle to be completed should be decreased. Is this correct or on the right track? Thanks.
 
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yep. Sounds good. (you can be more specific if you write down the mathematical relationship)
 

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