Thread: conceptualizing resonance.

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?

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

thanks.

Originally Posted by Naggy Doggy

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.