Final answer:
The appropriate state variables to determine the position of the mass in the system are the position variable (x) and the velocity variable (v). By tracking and analyzing changes in these state variables, the position of the mass can be determined.
Step-by-step explanation:
The appropriate state variables to determine the position of the mass in the system would be the position variable, denoted as x, and its derivative, the velocity variable, denoted as v. These variables are used to describe the motion of the mass in the system.
In the context of a mass-spring system, for example, the position variable x represents the displacement of the mass from its equilibrium position, while the velocity variable v represents the rate of change of position with respect to time.
By tracking and analyzing changes in these state variables, we can determine the position of the mass within the given system.