Understanding Normal Modes and Standing Waves in Vibrating Systems

[Raman Choudhary]

We know that in normal mode all the particles of the system vibrate with same frequency but if take a string fixed at both ends and make it vibrate in one of the normal modes in some cases we see nodes being formed at certain points and we say these are the points with zero amplitude but since the definition of normal mode says that all the particles must have same frequency so can we conclude that node does have zero amplitude but non zero frequency?? if yes isn't it weird (no vibration but a frequency).
Or else what is the correct definition of normal mode??

 

[blue_leaf77]

Don't sweat something like that, the saying that all parts of the string oscillate with the same frequency was made in reference to the mathematical expression of the mode frequency which does not depend on position. If you are not satisfied with that interpretation, it's not so wrong to pretend to never hear of it.

Or else what is the correct definition of normal mode??

It's the eigensolution of the system's equation of motion. The temporal behavior of eigensolution preserves its functional form throughout the course of the motion.