Oscillatory systems are physical systems that exhibit periodic motion, meaning they move back and forth around an equilibrium position. Common examples include a swinging pendulum, a vibrating spring, or the motion of a mass attached to a spring. These systems are characterized by their frequency, amplitude, and period, which describe how often they oscillate, how far they move from the equilibrium, and the time it takes to complete one full cycle, respectively. In many oscillatory systems, forces such as gravity or elasticity play a crucial role in restoring the system to its equilibrium position. The study of these systems is important in various fields, including mechanics, engineering, and physics, as they help us understand phenomena like sound waves, electrical circuits, and even the behavior of atoms in quantum mechanics.