Even after moving the weight, you can use the same spot to get the same amplitudes. Take at least eight sets of measurements for the arm length. Finally, decide on at least another parameter to vary. You'll have to make up your own procedure. Be sure to take good notes about what exactly you did, since you'll have to be clear in your lab report.
Analysis Examine the pendulum.
Use it to outline the forces that act on the pendulum. Examine your data. If the line through your data is straight but sloped, then there is a linear relationship between the parameter you varied and the period. In some cases, the data may be linear in some parts and non-linear elsewhere. Later in class we will develop the full theory that describes this type of motion.