Oscillator Ensemble

 

Damping, b=

Twenty-nine damped harmonic oscillators are driven by an external force,  sin(t).  Each oscillator can be thought of as a mass connected to the floor with a spring. The masses are not connected in any way. One spring has been shown for demonstration purposes.

The center oscillator, shown in red, is in resonance with the external force.  It has a natural frequency of oscillation of omega=1.  Oscillators to the left have a spring with a lower spring constant while those on the right have a larger spring constant.  This simulations shows how this collection of oscillators responds to the driving force.

The simulation starts with all oscillators at rest.  The oscillators then begin to move up and down in phase with the driving force during the first few cycles.  This motion is, however, transient and differing amplitudes and phases soon manifest themselves.  Since oscillators to the right of the center have a higher resonance frequency, they begin to lead the driving force while those to the left of center begin to lag.  Although the above oscillators are not connect, this phase shift gives the appearance of  a traveling wave.  After a few hundred oscillations the transient behavior has dissipated and a resonance curve appears as the amplitude and phase of each oscillator approach their steady state behavior.

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