Harmonic oscillator

related topics
{math, energy, light}
{math, number, function}
{car, race, vehicle}
{game, team, player}
{mi², represent, 1st}

In classical mechanics, a harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x according to Hooke's law:

where k is a positive constant.

If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).

If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:

  • Oscillate with a frequency smaller than in the non-damped case, and an amplitude decreasing with time (underdamped oscillator).
  • Decay exponentially to the equilibrium position, without oscillations (overdamped oscillator).

If an external time dependent force is present, the harmonic oscillator is described as a driven oscillator.

Mechanical examples include pendula (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. 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 vibrations and waves.

Contents

Full article ▸

related documents
Geodesy
List of relativistic equations
Phonon
Planets beyond Neptune
Doppler effect
Correspondence principle
Second law of thermodynamics
Newton's laws of motion
Twin paradox
Permittivity
Precession (astronomy)
Neutron star
Torque
Infrared
Comet Shoemaker-Levy 9
Oort cloud
Uranus
Warp drive
Quark
Main sequence
Brown dwarf
Electromagnetic field
Parallax
Frame of reference
Holographic principle
Orbital resonance
Roche limit
Event horizon
Ohm's law
Eclipse