The fourth harmonic of linear array of couples harmonic oscillators.
The fourth harmonic of linear array of couples harmonic oscillators.
"The investigation by John and Daniel Bernoulli [of the coupled oscillator chain] may be said to form the beginning of theoretical physics as distinct from mechanics, in the sense that it is the first attempt to formulate the laws of motion of a system of particles rather than that of a single particle." Leon Brillouin
Oscillator Chain models a one-dimensional crystal solid using a linear array of coupled harmonic oscillators. This model can be used to study the propagation of waves in a continuous medium and the vibrational modes of a crystalline lattice. The Ejs model shown here contains 31 coupled oscillators equally spaced within the interval [0, 2 π] with fixed ends. The m-th normal mode of this system can be observed by entering f(x) = sin( mx/2) as the initial displacement. Wave propagation can be studied by entering a localized pulse or by setting the initial displacement to zero and dragging oscillators to form a wave packet.
In interesting and important feature of the Oscillator Chain model is that the speed of a sinusoidal wave along the oscillator array depends on its wavelength. This causes a wave packet to disperse (change shape) and imposes a maximum frequency of oscillation (cutoff frequency) as is observed in actual crystals.