A physics class is conducting an experiment with a pendulum, which is suspended from a $3$meter rope attached to a ceiling $4$ meters above the ground. During the experiment, the pendulum is pulled to one side, reaching a maximum angle of pi$/3$ radians from the vertical. The pendulum takes $2$ seconds to swing from its resting position to this extreme point. Using the principles of harmonic motion, create a sinusoidal function to model the horizontal displacement of the pendulum, with the vertical hanging position defined as x$=0.$