Circular Motion lab problem

This is a question pertaining to a lab we did. Ill try to describe it the best i can. What we pratically did was attach a rubber stopper to an end of a string, put the string to a hollow tube (like a torn apart pen), and tied a mass on the bottom. We had to hold on the tube and start swinging the rubber stopper horizontally by rotating the tube. The mass tied to the string caused a tension force. It is impossible to have the stopper on the string spinning perfectly horizontal because perpindicular forces are independent of each other. We then had to calculate the frequency of the stopper while changing some variables.

Here is my question,

For the greatest accuracy in this investigation, the tension force acting on the tsopper should be horizontal. In this context, what happens to the accuracy as the frequency of revolution of the stopper increases (with the other variables held constant)?

i said as the frequency increases, the accuracy decreases, but i dont know how to explain why.