Final answer:
Repetitive motion through an equilibrium position is called simple harmonic motion, which is a periodical motion with a force that's proportional to displacement and directs an object back toward equilibrium.
Step-by-step explanation:
A repetitive motion through an equilibrium position is known as simple harmonic motion (SHM). This is a type of periodic motion where the restoring force is directly proportional to the displacement. It is a motion that repeats itself in a regular cycle, such as a pendulum swinging back and forth through its equilibrium position, or a guitar string vibrating around its central position. When an object is displaced from its equilibrium position, it experiences a restoring force, often due to elasticity or gravity, that directs it back toward that equilibrium position where the net force is zero.
In the context of a pendulum, the equilibrium position is the point where the pendulum bob hangs directly downward and is at rest. When the bob is lifted and released, it swings back towards this point due to gravity, which acts as the restoring force. The system's motion can then be described using properties such as amplitude, frequency, and period, all of which are characteristics of SHM.