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I have a question relating to uncertinity.The equation used is period of a pendulum.

T=2π √(l/g)

For example consider time to complete 10 cycles by the pendulum as 19.6 (+/- 0.2)s.
I want to know how to calculate the uncertinity of
1.period (T)
3.log T

Any help would be appriciated :)

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Hi SriniShine, and welcome to Physics Stack Exchange! Asking for answers to your homework questions is not allowed by our homework policy, but if you edit it to focus on the specific concept that is giving you trouble, it could be reopened. –  David Z Nov 11 '12 at 18:08
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closed as too localized by Qmechanic, David Z Nov 11 '12 at 17:54

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1 Answer

Given $X = f(A,B,C,\ldots)$ where $f$ is some function, the error in $X$ is given by

$$(\Delta X)^2= \left(\frac{\partial f}{\partial A}\cdot\Delta A\right)^2 + \left(\frac{\partial f}{\partial B}\cdot\Delta B\right)^2 + \left(\frac{\partial f}{\partial C}\cdot\Delta C\right)^2 + \cdots$$

where $\Delta i$ is the error in $i$.

So the period is given by

$$T = \frac{t}{n}$$

Where $t$ is the total time, and $n$ is the number of trials. So,

$$(\Delta T)^2 = \left(\frac{1}{n}\cdot\Delta t\right)^2+ 0$$

because $\Delta n$ is $0$.

Then apply same method to further functions of $t$ and $n$.

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You should check your error propagation formula. It's supposed to be the quadrature sum of those terms, not the linear sum. –  Chris White Nov 12 '12 at 7:37
Yeah, you're right. –  fophillips Nov 12 '12 at 12:10
thanks alot fophillips –  SriniShine Nov 14 '12 at 16:34
If you rephrase the question so it is more generally about error propagation it could be reopened. –  fophillips Nov 14 '12 at 16:49
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