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Simple harmonic motion can be considered the one-dimensional projection of uniform circular motion. If an object moves with angular speed ω around a circle of radius r centered at the origin of the xy-plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.
The motion is periodic, repeating itself in a sinusoidal fashion with constant amplitude A. In addition to its amplitude, the motion of a simple harmonic oscillator is characterized by its period = /, the time for a single oscillation or its frequency = /, the number of cycles per unit time.
The Hooke's atom is a simple model of the helium atom using the quantum harmonic oscillator. Modelling phonons, as discussed above. A charge q {\displaystyle q} with mass m {\displaystyle m} in a uniform magnetic field B {\displaystyle \mathbf {B} } is an example of a one-dimensional quantum harmonic oscillator: Landau quantization .
Harmonic motion can mean: the displacement of the particle executing oscillatory motion that can be expressed in terms of sine or cosine functions known as harmonic motion . 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 ...
Expansion in a Fourier series may provide an equation of motion to arbitrary precision. The term, also called the Duffing term, can be approximated as small and the system treated as a perturbed simple harmonic oscillator. The Frobenius method yields a complex but workable solution.
The restoring force is often referred to in simple harmonic motion. The force responsible for restoring original size and shape is called the restoring force. [1] [2] An example is the action of a spring. An idealized spring exerts a force proportional to the amount of deformation of the spring from its equilibrium length, exerted in a ...
Since the force acting on the oscillator is conservative and the motion occurs over a finite domain, the motion will be cyclic with some period which will be denoted T. Since the probability of the oscillator being at any possible position between the minimum possible x-value and the maximum possible x-value must sum to 1, the normalization
At sufficiently low temperatures and high magnetic fields, the free electrons in the conduction band of a metal, semimetal, or narrow band gap semiconductor will behave like simple harmonic oscillators. When the magnetic field strength is changed, the oscillation period of the simple harmonic oscillators changes proportionally.