Eigenfrequencies of a multiple DOF system

[aldo sebastian]

I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation between the eigenfrequencies of the system and the initial condition that you apply?

 

[sophiecentaur]

will it want

That implies a high degree of intelligence and anthropomorphism is not a useful approach.
If a system has multiple natural (orthogonal) modes and you excite it at one of those modes then it should vibrate at that frequency only. So that's your "initial conditions" idea. If the system is linear then it will stay that way but real systems, like musical instruments will end up changing frequency distribution over time.

 

[BvU]

Second centaur

Simple example: coupled pendula
swing both same way excites one mode,
swing in opposite ways excites the other

 

[sophiecentaur]

Second centaur

Simple example: coupled pendula
swing both same way excites one mode,
swing in opposite ways excites the other

And ideally there need be no transfer of energy from one mode to the other. A combination of both modes (say you start just one pendulum off on its own) will result in the classic situation with each pendulum going from maximum amplitude to near zero and back again as the result of the presence of the two modes.