Understanding Resonance in Mass-Spring Systems: A Visual Approach

[holtto]

In a mass-spring system that is driven by an external force, its displacement-time graph consists of several components.

One of them is Asin(bt), where b is the driving frequency and$$A=\frac{a}{w^{2}-b^{2}}$$

where w is the natural frequency.as b approaches w, A approaches infinity. however, i find the differential equation used to derive the above expression quite counter-intuitive. is there an easier to way to visualize resonance of a mass-spring system?

 

[holtto]

is there something to do with the oscillation of the system stabilizing itself?

 

[vanhees71]

We are discussing this issue right now in another thread. I've given the full solution of the equation and discussed the corresponding Green's function. This explains everything on this issue (see the posting, I've just written a minute ago :-)):

https://www.physicsforums.com/showthread.php?t=641304