A harmonic oscillator is a system that experiences a restoring force proportional to its displacement from an equilibrium position. This means that when the system is disturbed, it will oscillate back and forth around that position. Common examples include a mass on a spring or a pendulum. The motion is periodic, meaning it repeats at regular intervals. Harmonic oscillators are described mathematically by Hooke's Law, which states that the force exerted by the spring is equal to the negative product of the spring constant and the displacement. These systems are fundamental in physics and engineering, appearing in various applications like vibrations, waves, and even in quantum mechanics.