Forced Vibration: Amplitude Of Vibration Changes Periodically?

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Discussion Overview

The discussion revolves around the nature of amplitude in forced vibration, specifically whether the amplitude changes periodically and how it relates to the periodic function of displacement. Participants explore the implications of terminology and the behavior of amplitude over time in forced vibration scenarios.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that the amplitude of vibration changes periodically, suggesting it is a correct statement due to its nature as a periodic function.
  • Others argue that while displacement is a periodic function, amplitude, defined as the maximum displacement, is not periodic.
  • A later reply questions whether the amplitude of forced vibration decays exponentially over time.
  • Another participant explains that in forced vibration, a steady frequency leads to exponential growth in amplitude until a maximum is reached, followed by exponential decay when excitation is removed, with no change in frequency except for possible ringing.

Areas of Agreement / Disagreement

Participants express differing views on the periodic nature of amplitude in forced vibration, with some asserting it is periodic and others contesting this claim. The discussion remains unresolved regarding the characterization of amplitude.

Contextual Notes

There appears to be a terminology confusion regarding the definitions of amplitude and displacement, which may affect the interpretation of the claims made. The discussion also touches on the behavior of amplitude over time, including growth and decay, but lacks consensus on these points.

roshan2004
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In forced vibration, amplitude of vibration changes periodically. Is it right ? I think it is a correct statement, since the amplitude of vibration is a periodic function.
 
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Are you suggesting that you get a 'beat'?
You don't get a beat, just a reduced amplitude of response. The level will depend on the Q of the resonator and the frequency offset.
 
roshan2004 said:
In forced vibration, amplitude of vibration changes periodically. Is it right ? I think it is a correct statement, since the amplitude of vibration is a periodic function.
I think there may be a bit of a terminology confusion here. The displacement is a periodic function in vibration. The amplitude is the maximum displacement, so it is not periodic.
 
So, does it decays exponentially then... ( I mean amplitude of the forced vibration)
 
The term 'forced vibration' means that a steady vibration frequency is applied. The result is a 1/exponential growth in amplitude takes place over time, until a max amplitude is reached. When the exitation is removed, there is an exponential decay in amplitude. There is no change in frequency at any time except for a small possible 'ringing' due to a discontinuity on switch on and switch off. But that is not usually considered.
 

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