How is Uncertainty Propagated in Pendulum Period Measurements?

In summary, the conversation discusses measuring the period of a pendulum and its consistency with the true period. The calculated value for g involves both errors in the measurement of the pendulum's length and the period. The speaker also mentions using a simulation on the computer and the calculation involved in finding g.
  • #1
RaamGeneral
50
1
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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  • #2
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 .
 
  • #3
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.
 

Related to How is Uncertainty Propagated in Pendulum Period Measurements?

What is propagation of uncertainty?

Propagation of uncertainty is a statistical method used to estimate the uncertainty or error in a calculated result based on the uncertainties in the input variables. It takes into account the correlations between the input variables and uses mathematical formulas to determine the range of possible values for the final result.

Why is propagation of uncertainty important?

Propagation of uncertainty is important because it allows scientists to quantify and communicate the level of uncertainty in their experimental results. This is crucial for making informed decisions and drawing accurate conclusions from the data.

How is propagation of uncertainty calculated?

Propagation of uncertainty involves using the partial derivative of the calculated result with respect to each input variable, along with the uncertainties in those variables, to determine the overall uncertainty in the final result. This can be done using various mathematical formulas, such as the Taylor series expansion or the Monte Carlo method.

What factors affect the propagation of uncertainty?

There are several factors that can affect the propagation of uncertainty, including the number and type of input variables, the correlation between those variables, and the sensitivity of the calculated result to each variable. Additionally, the method used to calculate the uncertainty can also impact the final result.

How can propagation of uncertainty be reduced?

Propagation of uncertainty cannot be completely eliminated, as it is inherent in any measurement or calculation. However, it can be reduced by increasing the precision and accuracy of the input variables, reducing the correlations between variables, and using more accurate and precise methods to calculate the uncertainty. Additionally, conducting multiple trials and averaging the results can also help reduce the overall uncertainty.

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