In a well-designed experiment, it is crucial to control variables to ensure that the results accurately reflect the relationship being tested. In the experiment you described, where the goal is to determine how the arm length of a pendulum affects its period, the correct approach is to keep all other variables constant while varying the independent variable (in this case, the arm length).
Therefore, the statement that aligns with good experimental design is:
Only the arm length should be changed. The mass should remain the same.
This ensures that any changes in the period of the pendulum can be attributed solely to changes in the arm length, allowing for a clear understanding of its effect.