Error calculations involving gradients

by acidburner
Tags: calculations, error, gradients, involving
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 P: 1 I'm trying to work out the percentage error in working out the value of gravity,g, from a pendulums motion. i know that percentage error is (possible error/value used)*100 however im using multiple values multiple times and its getting a little confusing. In the investigation g=k(∆Tē/∆L), my problem is that i have the error for working out T which is 0.001 seconds. The error in L is 0.001m. As i'm using a difference of two values for each of the ∆'s would i double each error and for the error of Tē would i square 0.001 and then double it. any explainations would be helpful Thanks ∆Tē=2.112 ∆L=0.51
 HW Helper P: 6,202 You know that $$T=2\pi \sqrt{\frac{l}{g}}$$ so that $$T^2=4\pi^2 \frac{L}{g}$$ and that means that $$g=\frac{4\pi^2}{T^2}L$$ To find the error you do this. $$\frac{\delta g}{g}=2\frac{\delta T}{T} + \frac{\delta L}{L}$$ $\delta T$ would be the error in T and similarly for $\delta L$ is the error in L.

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