# Eigenfrequencies of a multiple DOF system

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
Gold Member
2020 Award
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
BvU
Homework Helper
Second centaur

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

sophiecentaur
sophiecentaur