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The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used as toy problems that describe many physical systems.
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Physical Meaning of two solutions when asking Angular Frequency of a System as a Function of...
Introduction
Take the Forced Harmonic Oscillator of a spring:
$$ \ddot x + 2\Gamma \dot x +\omega_0^2 x = f_0 \cos(\omega t) $$
where $\omega_0$ is the natural frequency $\sqrt{\frac{k}{m}}$, $\omega …