A harmonic oscillator is a physical system that has a repeating pattern of motion, which is described by a mathematical function called a sine or cosine function. This type of motion is known as simple harmonic motion.
A harmonic oscillator works by having a restoring force that pulls it back to its equilibrium position when it is displaced from it. This restoring force is proportional to the displacement, resulting in a periodic motion around the equilibrium point.
Some examples of harmonic oscillators include a simple pendulum, a mass-spring system, and a vibrating guitar string. These systems all have a restoring force that follows a sine or cosine function, resulting in simple harmonic motion.
The equation for a harmonic oscillator is given by F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position. This equation is also known as Hooke's law.
A harmonic oscillator follows a sinusoidal pattern of motion, while a non-harmonic oscillator does not. Non-harmonic oscillators have restoring forces that do not follow a simple mathematical function, resulting in more complex motion patterns.