Forced oscillations of a linear system

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Discussion Overview

The discussion revolves around the behavior of a chain of metal bars connected by nylon wire, specifically focusing on the forced oscillations and the unexpected frequency components observed during experimentation. The scope includes experimental analysis and theoretical considerations related to wave propagation and normal modes.

Discussion Character

  • Experimental/applied
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant describes an experiment where a chain of metal bars is excited at non-normal mode frequencies, leading to unexpected frequency peaks in the Fourier spectrum, including a significant peak at three times the driving frequency.
  • Another participant questions whether the analysis of wave propagation considers the rotational moment of inertia of the metal bars, suggesting that this could lead to mode conversion.
  • The original poster acknowledges not accounting for rotational inertia and speculates that the bars may oscillate in multiple directions due to their attachment to the nylon wires, which could affect the oscillation behavior.
  • A participant seeks clarification on the term "mode conversion," indicating a need for further understanding of the concept.

Areas of Agreement / Disagreement

Participants have not reached a consensus. There are differing views on the factors influencing the observed oscillation behavior, particularly regarding the role of rotational inertia and the concept of mode conversion.

Contextual Notes

The discussion highlights potential limitations in the theoretical analysis, including the neglect of rotational inertia and the complexity of oscillation modes in the experimental setup. The implications of these factors on the observed frequency peaks remain unresolved.

watty
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Hello,

I am currently working on a lab in which we are studying the behaviour of chain of metal bars attached together with nylon wire in such a way as to to mimic the ability of solids or liquids to transmit a wave.

After studying the normal modes of the system as well as the quality factor, we excited the system at frequencies not equal to normal modes and analysed the frequencies present using an optical detector wired through a computer that can perform a Fourier analysis of the spectrum.

When the system was being driven, we expected to see only one frequency present in the Fourier spectrum: that of the driving oscillator. However we also saw two very small peaks at normal frequencies as well as a significant peak at what appeared to be 3 times the driving frequency.

The two small peaks I can understand as maybe imperfections of the system, ie the forced oscillation does not fully overcome the natural properties of the system but I don't understand why the system is also oscillating at 3 times the driving frequency.

NB. there is also a normal mode reasonable close to this significant unexplained peak.
 
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When you theoretically analyze the propagation of waves in this chain, are you fully accounting for the rotational moment of inertia in the individual metal bars? The metal bars have both center-of-mass motion (linear inertia) and rotational inertia. Could this cause mode-conversion?
Bob S
 
no i have not taken this into account. you mean that they are oscillating not just on one axis but in several directions? this could be the case. each metal bar is attached at each end to two long nylon wires. the wires are at high tension but there could be some extension and contraction in the wires and i suppose the bars are not moving exclusively up and down but also left and right too. Is this what you mean?
 
ps. mode conversion? what does this mean?
 

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