Calculating Uncertainty in Spring Period Measurement

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SUMMARY

The discussion focuses on calculating the uncertainty in the period of a spring using the formula T = 2π√(x/g), where x represents the extension of the spring. The measured extension is given as x = 0.10m ± 0.01. The correct approach to determine the uncertainty in the period (σT) is confirmed to be σT = dT/dx * σx, where dT/dx is the derivative of the period with respect to the extension.

PREREQUISITES
  • Understanding of basic physics concepts, specifically Hooke's Law.
  • Familiarity with calculus, particularly differentiation.
  • Knowledge of uncertainty propagation in measurements.
  • Basic understanding of gravitational effects on spring systems.
NEXT STEPS
  • Study the principles of Hooke's Law and its applications in spring mechanics.
  • Learn about uncertainty propagation techniques in experimental physics.
  • Explore calculus, focusing on differentiation and its applications in physics.
  • Investigate the effects of gravity on oscillatory motion in spring systems.
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Physics students, experimental researchers, and anyone involved in mechanical systems analysis will benefit from this discussion.

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I want to calculate the uncertainty in the period for a spring, when I have measured the extension of it under the influence of gravity.
Call that x and say I got:
x=0.10m ± 0.01
And we know that:
T = 2∏√(x/g)
Is it then correct to use the following formula for the uncertainty σT:
σT = dT/dx * σx
 
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That would work, yep.
 

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