In normal modes analysis the differential equations of the system are Fourier transformed and the Fourier monochromatics are found. I think these monochromatics are usually called normal modes of the system.
However, often, the monochromatics by themselves aren't solutions of the equations (but the solutions can be decomposed in monochromatics). Often it is written that the system can oscillate at the normal mode frequency, but if the monochromatic is not a solution this can't be true.
Probably there is something that I'm misunderstanding, can you give me a clarification?
