Eigenfrequencies of a multiple DOF system

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Discussion Overview

The discussion revolves around the concept of eigenfrequencies in a multiple degree of freedom (DOF) system, exploring how these frequencies relate to the system's behavior under various initial conditions. Participants examine the implications of exciting different modes and the resulting vibrational characteristics of the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how a system with multiple eigenfrequencies determines which frequency it will vibrate at, questioning the role of initial conditions.
  • Another participant challenges the anthropomorphism in the phrasing "will it want," suggesting that if a system is excited at a specific mode, it will vibrate at that frequency, particularly in linear systems.
  • A participant provides a simple example of coupled pendula to illustrate how different initial conditions can excite different modes, noting that swinging both pendula the same way excites one mode while swinging them oppositely excites another.
  • Further elaboration on the coupled pendula example indicates that ideally, there should be no energy transfer between modes, and a combination of initial conditions can lead to a classic oscillatory behavior between the two modes.

Areas of Agreement / Disagreement

Participants present differing views on the interpretation of how initial conditions affect vibrational modes, with some emphasizing the linearity of systems while others highlight the complexities of real-world applications. The discussion remains unresolved regarding the precise relationship between initial conditions and eigenfrequencies.

Contextual Notes

There are limitations in the discussion regarding assumptions about linearity and the behavior of real systems, as well as the dependence on specific definitions of eigenfrequencies and modes.

Who May Find This Useful

This discussion may be useful for students and professionals in physics and engineering who are exploring the dynamics of systems with multiple degrees of freedom and the implications of eigenfrequencies in practical applications.

aldo sebastian
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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?
 
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aldo sebastian said:
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.
 
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Second centaur

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

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