# Error Analysis/Significant Figure help please

1. May 29, 2013

### MassivePhysics

Hi Physics Forums,

I have an assignment due very soon and I have completed everything, bar error analysis. I have been told that we need to calculate relative and absolute errors or something along those lines and I have NO IDEA what im doing. I have been researching the topic and searching forum threads, but to no avail. Please someone help me!

Basically, I have calculated the local acceleration of gravity via a pendulum experiment. I have measured various lengths of fishing line which I have dropped and recorded the time of 5 periods for.
I have plotted the average period for 5 different lengths of fishing line, squared (T²) against the lengths of the fishing line (L). I have measured the average period to 4 significant figures (e.g 4.033, 4.267 etc) and the length to two significant figures (e.g 4.0, 4.5, 5.0) etc. The lengths were measured using a tape measure with 10cm intervals and the stopwatch used to record the period had 2 decimal places. (Although the stopwatch only had 2 decimal places, the period values have 3 decimal places as they were recorded based on 15 periods and then divided by 15, so the 15 periods had 2 decimal places but 4 significant figures).

How on earth do I do an error analysis??

Any help would be great.

Thanks.

2. May 29, 2013

### Simon Bridge

It's a little late ... here's a crash course:

The absolute error is the standard deviation of your results.
The relative error is the absolute error divided by the mean value.

A typical experiment would measure the time for 10 (or so) periods for each length.
You would notice that these times are slightly different ... so you take the average and the standard deviation of the measurements ... these are the time and the absolute error on the time.
Divide both by 10 to get the period and the absolute error on the period.

You also measured the length of the string - which you should also do several times before and after the experiment... or you can guess the absolute error to be half the smallest deviation on the ruler.

This should start to sound familiar to you.

If the absolute error in measurement $x$ is $\sigma(x)$ and the relative error is $r(x)$ then:

$r(x)=\sigma(x)/x\\ \sigma(x+y)=\sqrt{\sigma^2(x)+\sigma^2(y)}\\ r(xy)=\sqrt{r^2(x)+r^2(y)}\\ \sigma(ax)=a\sigma(x)\\ r(x^n)=nr(x)$

You should have some notes on this from your coursework.