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The harmonic oscillator model is very important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal ...
In mechanics and physics, simple harmonic motion (sometimes abbreviated as SHM) is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position.
Here we show that a necessary condition for stable, exactly closed non-circular orbits is an inverse-square force or radial harmonic oscillator potential. In the following sections, we show that those two force laws produce stable, exactly closed orbits .
Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.
These equations represent the simple harmonic motion of the pendulum with an added coupling factor of the spring. [1] This behavior is also seen in certain molecules (such as CO 2 and H 2 O), wherein two of the atoms will vibrate around a central one in a similar manner. [1]
This is a form of the simple harmonic oscillator, and there is always conservation of energy. When μ > 0 , all initial conditions converge to a globally unique limit cycle. Near the origin x = d x d t = 0 , {\displaystyle x={\tfrac {dx}{dt}}=0,} the system is unstable, and far from the origin, the system is damped.
The motion of a Harmonic oscillator (in physics), which can be: Simple harmonic motion; Complex harmonic motion; Keplers laws of planetary motion (in physics, known as the harmonic law) Quasi-harmonic motion; Musica universalis (in medieval astronomy, the music of the spheres) Chord progression (in music, harmonic progression)
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point , it is one of the most important model systems in quantum mechanics.