Final answer:
The appropriate control variable for this experiment is the period.
Step-by-step explanation:
The appropriate control variable for this experiment would be option A. the period. In an experiment, the control variable is the variable that is kept constant or unchanged throughout the experiment. In this case, the period refers to the time it takes for the ball to swing forward and back to its starting position. By keeping the period constant while varying the string lengths, the student can observe the effect of the string lengths on the period.