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A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
For any simple mechanical harmonic oscillator: ... Using the techniques of calculus, the velocity and acceleration as a function of time can be found: () ...
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.
Harmonic oscillator; ... and each is a function of time. ... where v j is the velocity of the point of application of the force F j.
The probability density function of the n = 30 state of the quantum harmonic oscillator. The solid plot represents the quantum mechanical probability density, while the dotted line represents the classical probability density. The dashed vertical lines indicate the classical turning points of the system.
The simplest description of this decay process can be illustrated by oscillation decay of the harmonic oscillator. Damped oscillators are created when a resistive force is introduced, which is dependent on the first derivative of the position, or in this case velocity.
Suppose the Hamiltonian of a harmonic oscillator is given by = + with momentum,; mass,; angular frequency, and; displacement,; then the Fradkin tensor (up to an arbitrary normalisation) is defined as
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...