Traveling Waves on an Oscillator Chain

Driven Oscillator Chain models a one-dimensional linear array of coupled simple harmonic oscillators driven at one end and attached to a sliding rod shock absorber at the other. The mass and damping of the shock absorber are chosen to eliminate reflections at the driving frequency.

A traveling wave propagates along the oscillator chain in the positive x-direction with a wave function Φ(x,t) that depends on position and time 

 

where A is the amplitude, ω=2πf is the angular frequency, and k=2π/λ is the wave number.  The angular frequency and wave number are related though the dispersion relationship

.

An interesting and important feature of this dispersion relationship is that it predicts a maximum frequency wH=(4K/M)1/2.  What type of motion is observed if the diving frequency is greater than this maximum?

References:

The coupled oscillator (beaded string) model is discussed in most intermediate mechanics textbooks.

There are many laboratory and computer experiments that build on the beaded string model.

Note:

This simulation was created by Wolfgang Christian using the Easy Java Simulations (Ejs) modeling tool. You can modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu. Information about Ejs is available at: <http://www.um.es/fem/Ejs/>.