Here's what I'm doing: I'm using MATLAB to model a ball placed within a potential energy well. I'm then driving this ball with an external driving force. The function for the external driving force and the shape of the potential energy curve are both defined by me. Once I drive the ball within the potential with my customized driving force, I look at the ball's motion and take a Fourier Transform to see what frequency components make up it's motion.
If I place the ball in a parabolic potential well and drive it with some frequency, I get two peaks in the Fourier Transform: one for the frequency at which I'm driving the ball, and another peak that corresponds to the resonant freuqency of my potential well (in this case a parabola).
What's interesting is that if I drive it with two different frequencies, then most of the time I get 3 peaks, two corresponding to the two different frequencies that I'm driving the ball with, and the last one being the constant resonant frequency of the potential.
This rule holds for most pairs of driving frequencies, with one big exception. Any two frequencies of the form (f, (resonanting frequency^2)/f) leads to only 2 peaks! The resonant peak goes away! In the case where the mass of the ball is 1, the resonant frequency is sqrt(2), thus for mass = 1, any two driving frequencies of the form (f,2/f) lead to no amplitude at sqrt(2), so take for example 1Hz and 2Hz:
What is the explanation for the disappearance of this peak? Why must the two driving frequencies be of the form listed above???