How is Uncertainty Propagated in Pendulum Period Measurements?

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SUMMARY

The discussion centers on the propagation of uncertainty in pendulum period measurements, specifically using the formula for gravitational acceleration (g). The measured period is T = 2.18 ± 0.02 seconds, leading to a calculated g value of 9.96 ± 0.2 m/s². The length of the pendulum is stated as 1.20 meters with no associated error. The calculation of g involves determining the slope from the relationship L = g/(4π²) * T², highlighting the importance of accurate period measurements for precise gravitational calculations.

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RaamGeneral
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Hello.
I have measured the period of the pendulum
T=2.18 +/- 0.02

which is consistent with the true period 2.19865... so I expect myself to find a consistent value of g if I apply the formula propagating the error in the right way.

I get
g=9.96 +/- 0.2Why?
 
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Assuming you are referring to a simple pendulum what is it's length, and the error in that measurement? The final calculated value for g will involve both errors .
 
Thanks for your reply. Length is 1.20 meter without error. I'm training myself with a simulation on computer. The problem here is calculation, I discovered that usually to find g, we find the slope of the line L = g/4pi^2 * T^2
I also noticed that if i take T = 2.20 and T = 2.16, and I calculate g, the real value is between them.
 

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