Understanding Resonance in Mass-Spring Systems: A Visual Approach

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In a mass-spring system driven by an external force, the displacement-time graph includes components like Asin(bt), where b is the driving frequency and A is dependent on the natural frequency w. As b approaches w, A tends toward infinity, indicating resonance. The discussion highlights the counter-intuitive nature of the differential equation used to derive this relationship and seeks a clearer visualization of resonance. There is mention of another thread discussing the full solution and Green's function related to this topic. The conversation emphasizes the complexities of understanding resonance in mass-spring systems.
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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 andA=\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?
 
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is there something to do with the oscillation of the system stabilizing itself?
 
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
 
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