Hi, I'm trying to understand vibrations and specifically what happens in the natural modes of frequency.. 1. It seems that the harmonic nature of solution(with Acos(wt)...where A is the amplitude) applies only in the natural mode of vibration...and so the system will have a defined mode shape only in its natural mode?...what happens otherwise? 2. A system with 2 degrees of freedom has 2 resonant frequencies.....what are these frequencies...meaning is the first resonant frequency a characteristic of the first vibrating particle/body and the second one is a characteristic of the second body? ..intuitively, why is it necessary for the no. of degrees of freedom to be equal to the number of resonant frequencies available? 3. Also, how is it possible to excite multiple natural frequencies simultaneously...like in a violin string? ...since its hard to image how they can coexist on the same string. Thanks in advance for your help.