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Thread: conceptualizing resonance.

  1. #1 conceptualizing resonance. 
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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 and

    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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    this may help http://math.bd.psu.edu/faculty/jprev...bookSec3.6.pdf


    “The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.”

    Bertrand Russell
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  4. #3  
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    thanks.
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    Quote Originally Posted by Naggy Doggy View Post
    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

    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?
    If you add more net energy per unit time than is dissipated, the amplitude will grow without bound. Resonance in a lossless spring-mass system (or inductor-capacitor system, or any number of analogues) describes just such a condition.
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