
A comparison of fifty-one driven simple harmonic oscillators with differing natural frequencies.
The driven harmonic oscillator is a standard physics model and the Driven SHO Comparison model displays 51 such oscillators with different natural frequencies driven. The oscillator mass increases from left to right in the multi-oscillator display and the oscillator in the center has a mass of one. All 51 oscillator differential equations are solved simultaneously but the motion or each oscillator is independent of the others because these equations are uncoupled.
where k is the spring constant, b is the damping coefficient, and ω is the frequency of the sinusoidal force. Because the spring constant k and the frequency ω are set equal to one in the model, the natural frequency of oscillation of the center mass coincides with the drive frequency. The time step is chosen to be exactly 1/20 of the drive ω frequency so that 20 clicks of the single-step button advance the model by one drive period.
Run the simulation and note the red arrow to the left of the oscillators showing the driving force that is applied to each oscillator.
The Driven SHO Comparison JavaScript Model was developed by Wolfgang Christian using the Easy Java/JavaScript Simulations (EjsS) modeling tool version 5.1. Information about Ejs is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.