If measurements over a large range of slider positions are performed, a graph of the two periods versus slider position should look like that provided in Figure 5. Of course, such a wide range of slider positions is not necessary to estimate g. As previously mentioned, only four or five positions are really required. Period versus Slider position in the vicinity of period matching. Here, using Excel, a linear regression has been separately performed on each of the T 1 data and the T 2 data.
Individual points correspond to the mean value of the period at a given slider position.
Then the estimate for g, along with its uncertainty is obtained from the following equations. It is well known for the Kater pendulum that the system is equivalent to a simple pendulum of length l m when the two periods are the same. Thus the method is typically two or three times more accurate than the quick method.