Forced Vibration: Amplitude Of Vibration Changes Periodically?

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SUMMARY

In forced vibration, the amplitude of vibration does not change periodically; rather, it is the displacement that is a periodic function. The amplitude represents the maximum displacement and is not periodic itself. The behavior of forced vibration is characterized by an exponential growth in amplitude over time until a maximum is reached, followed by an exponential decay when the excitation is removed. The quality factor (Q) of the resonator and frequency offset influence the amplitude response, but frequency remains constant during forced vibration.

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  • Familiarity with the concept of amplitude and displacement
  • Basic grasp of exponential growth and decay in oscillatory systems
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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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