We are used to the notion of classical harmonic oscillators; these are oscillators fluctuating coherently-this is, symmetrically-around their equilibrium position, experiencing a restoring force F proportional to the displacement x following the relationship F = – kx, being k a positive constant commonly known in the mechanics of ideal springs.
If F is the only force acting on the system (which means there is no friction with the environment) the system is called a simple harmonic oscillator, and it undergoes a sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency that does not depend on the amplitude.
In real life, for example in the case of a spring, we see a damped oscillation because it will decrease with time due to friction. So basically, the harmonic oscillation is a very useful idealization that allows to simplify many physical problems.
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