How Can You Calculate the Original Length of a Simple Pendulum?

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SUMMARY

The original length of a simple pendulum can be calculated using the formula T = 2π√(l/g), where T is the period of one oscillation, l is the length, and g is the acceleration due to gravity. In the discussion, a pendulum executed 100 oscillations in 375.6 seconds, leading to a period of 3.756 seconds. By applying the formula and adjusting for the reduced lengths of 50, 100, 150, 200, and 250 cm, the original length can be determined through systematic calculations or graphing methods.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with the formula T = 2π√(l/g)
  • Basic algebra for solving equations
  • Knowledge of gravitational acceleration (g ≈ 9.81 m/s²)
NEXT STEPS
  • Calculate the period of oscillation for various lengths using T = 2π√(l/g)
  • Explore the impact of changing lengths on oscillation periods
  • Learn how to graph the relationship between length and period
  • Investigate the effects of air resistance on pendulum motion
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of pendulums and simple harmonic motion.

John O' Meara
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A simple pendulum of unknown length was found to execute 100 oscillations in 375.6s. The length was then reduced by 50,100,150,200 and 250cm, and the corresponding times of 100 oscillations were found to be 347.7, 317.4,283.9, 245.9 and 200.7: find by calculation the original length of the pendulum?
The only formula I know is T=2(pi)sqr(l/g), I have no idea of how to start. Thanks in advance.I can always plot a graph and find it, but I do not know by calculation.
 
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You have the right idea, remember that T is the period for one oscillation so we need to divide by time by the number of oscillation and then solve for the length. To check your results plug in the length and try subtracting the given information, and see if you get the new periods when the length is shortened. Hope this helps, sincerely x
 

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