Problem
You want to test experimentally whether the period of a pendulum depends on the mass. For each element, state whether it is an independent, dependent, confounding, or controlled variable: (a) the mass hung on the string; (b) the length of the string; (c) the room temperature; (d) the measured period; (e) the initial oscillation amplitude.
Solution
Let us recall the definitions. The independent variable is the quantity the experiment deliberately varies in order to study its effect. The dependent variable is the quantity that is measured and that (possibly) changes in response. A controlled variable is held fixed throughout all trials, so as not to bias the comparison. A confounding variable is a quantity that could influence the result but is neither varied nor rigorously held fixed: if uncontrolled, it introduces scatter or errors.
Let us apply this scheme to the pendulum experiment, whose purpose is to see whether the period changes as the mass varies.
(a) The mass hung on the string → independent. This is precisely the quantity we choose to vary, so it is the independent variable of the experiment.
(b) The length of the string → controlled. The pendulum’s period depends strongly on ; to isolate the effect of the mass alone we must keep rigorously fixed.
(c) The room temperature → confounding. We do not vary it on purpose nor control it strictly; it could, however, influence the measurement (thermal expansion of the string, air density). It is thus a typical confounding variable.
(d) The measured period → dependent. This is the quantity we read off the stopwatch and whose possible variation we want to study: the dependent variable.
(e) The initial oscillation amplitude → controlled. For small oscillations the period is almost independent of it, but for a clean comparison it is kept constant (small and equal across all trials): it is a controlled variable.
In summary: