Sunday, May 8, 2011

Simple Harmonic Motion

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential equation
where x^.. denotes the second derivative of x with respect to t, and omega_0 is the angular frequency of oscillation. This ordinary differential equation has an irregular singularity at infty. The general solution is
where the two constants A and B (or C and phi) are determined from the initial conditions.
Many physical systems undergoing small displacements, including any objects obeying Hooke's law, exhibit simple harmonic motion. This equation arises, for example, in the analysis of the flow of current in an electronic CL circuit (which contains a capacitor and an inductor). If a damping force such as Friction is present, an additional term betax^. must be added to thedifferential equation and motion dies out over time.

Weisstein, Eric W. "Simple Harmonic Motion." From MathWorld--A Wolfram Web Resource.


Ulla said...

Harmonic oscillations are also mentioned behind the quantum world and solitons.

t'Hooft among others. colors, electroweak force?

Steven Colyer said...

Kay Zum Felde likes your comment very much on Facebook.

Ulla said...

Given the speculative connections to quantum mechanics mentioned above it is natural to wonder if
this [the quantization] is related to the zero point energy of the harmonic oscillator.

Michael Aityah: