# Error calculations involving gradients

1. Mar 31, 2008

### acidburner

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(∆T²/∆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 T² would i square 0.001 and then double it.
any explainations would be helpful
Thanks
∆T²=2.112 ∆L=0.51

2. Mar 31, 2008

### rock.freak667

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.