The motion executed by a torsional pendulum is classified as

In a torsional pendulum, the restoring torque $\tau$ is directly proportional to the angular displacement $\theta$ and is directed towards the mean position. This is given by the equation:

$\tau = -C\theta$

where $C$ is the torsional constant of the suspension wire.

This equation is the defining condition for angular simple harmonic motion.

Since the pendulum undergoes to-and-fro motion about a stable equilibrium position, the motion is oscillatory. Furthermore, because this motion repeats itself after a fixed interval of time, it is also periodic.

Therefore, the motion executed by a torsional pendulum is classified as angular simple harmonic, oscillatory, and periodic.