What is causing the loss of tracking in my spring-mass system?

[courtjester14]

Hi everyone! This is my first post here at PF after years of on & off lurking!

So, I'll get straight to it. At work (yes work, not HW) I have a forcing function signal that acts on a spring-mass system. When the spring-mass system "tracks" the forcing function, the curves overlap. However, as frequency is increased to a point, the amplitude of the response signal increases, and then loses "tracking". When it loses tracking, we see a signal that is the same frequency as the forcing function, but two things are evident: it is a composite of some combination of signals and there appears to be a beat phenomena.

So anyway, I just purchased a book on vibration because I had sold mine in college for food. Before it gets here, maybe I could get some suggestions as to what I should look for? I am specifically looking to place a function to the response signal. I'll draw up a quick picture in non-other than MS Paint.

*The black is the forcing function (simple sine wave) and the blue is the response. Top is tracking, bottom is loss of tracking*

Thank you for your help!

 

[Valerie Park]

It sounds like you may be dealing with a phenomenon known as resonance. Resonance is a type of oscillation that occurs when an external force is applied to a system and the frequency of that force matches the natural frequency of the system. When this happens, the amplitude of the response increases significantly compared to the amplitude of the external force. This can cause the system to 'lose tracking' of the external force.To understand this better, I'd suggest reading up on the basics of resonance and vibration. You may also find it helpful to look into the mathematics behind resonance, such as Fourier analysis or transfer functions. These mathematical tools can help you better understand the behavior of your system and can help you identify the underlying components of the response signal.