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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.
Plot of the spherical harmonic (,) with = and = and = in the complex plane from to + with colors created with Mathematica 13.1 function ComplexPlot3D In acoustics , [ 8 ] the Laplace spherical harmonics are generally defined as (this is the convention used in this article) Y ℓ m ( θ , φ ) = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) !
A simple, yet effective animated demonstration of a simple harmonic oscillator. Articles in which this image appears Simple harmonic motion , Harmonic oscillator , Effective mass (spring-mass system) , Sine wave , Oscillation , Vibration
In mechanics, as a linear motion over time, this is simple harmonic motion; as rotation, it corresponds to uniform circular motion. Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation.
The motion is simple harmonic motion where θ 0 is the amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical). The corresponding approximate period of the motion is then
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 .
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 ...