Harmonic Oscillator

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Introduction[✎ edit | edit source]

Harmonic oscillatory movement describes movement in which an object that has been displaced from its point of equilibrium is acted upon by a restoring force directly proportional to the amount of displacement. The classic model of such a movement is a weight attached to a spring, oscillating between the two extremes of maximum compression and maximum extension. In a simple (ideal) system as described, no energy is lost and the weight will oscillate for an infinite amount of time between the two extremes [1]. Based on these principles, the position, velocity, and acceleration of such a weight can be modeled by sinusoidal equations, as demonstrated below [2].

Simple harmonic oscilator - example

Equations[✎ edit | edit source]

Equations used to model simple harmonic oscillation in the case of a spring include:

  • Restoring force: F = -k·x

k is the spring constant; x is the displacement from position of equilibrium; F is the restoring force [1]

  • Position of the body: y = A·sin(ω·t + φ)

Y is position relative to the point of origin; A is maximum elongation; ω is angular frequency (given by ω=2·π·ƒ=(2·π)/T); T is the time to make one full oscillation; φ is the phase difference which gives the position of the body at T = 0 and its direction [2]

  • Maximum velocity: Vmax = A·ω [3]
  • Instantaneous velocity: V = Vmax·cos(ω·T) [3]

Links[✎ edit | edit source]

Related Articles[✎ edit | edit source]

External links[✎ edit | edit source]

Bibliography[✎ edit | edit source]

  1. a b University of Winnipeg. Simple Harmonic Motion [online]. ©1997. The last revision 1997-09-10, [cit. 2012-12-10]. <Simple Harmonic Motion>.
  2. a b Proyecto Newton. MEC. SIMPLE HARMONIC MOVEMENT [online]. ©2012. [cit. 2012-12-10]. <Simple Harmonic Movement>.
  3. a b AMLER, Evžen. Acoustics [lecture for subject Biophysics, specialization General Medicine, The 2nd faculty of medicine Charles University in Prague]. Prague. 2012-11-12.  .