Factors that influence period

In this section, we will explore what factors determine the period and the frequency.

$5\mathrm{.}1.$ Dependence of period on amplitude

You will first determine the effect of amplitude on period. Consider the following student discussion about this effect:

Alice: I think as you increase the amplitude, the period will also increase. Since the cart has further to go$,$ it will take longer to travel from its maximum position to rest and then to its maximum amplitude in the other direction. So the overall period increases when the amplitude increases.

Bertha: I think the period won't depend on amplitude at all. Sure, the cart travels further, but it's also going faster. These two effects will balance, and the period stays the same.

Colin: You have to think about the forces acting on the cart to decide. When we increase the amplitude, the spring is stretched more, and so it exerts a greater force. By Newton's second law, bigger forces cause larger accelerations. Since the acceleration is larger, the time for one complete cycle has to decrease.

With which, if any, of the above students do you agree?