Inquiry about Damped Oscillators

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    Damped Oscillators
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SUMMARY

The discussion focuses on the behavior of the full-width-half-maximum (FWHM) of resonance in forced and damped oscillators in relation to the Q-factor. It establishes that the amplitude of a forced and damped harmonic oscillator does not become infinite at resonance, despite the frequencies of the force and oscillator being equal. The Q-factor, which quantifies the damping of the oscillator, plays a crucial role in determining the bandwidth and resonance characteristics. A reference to Wikipedia on the Q factor provides additional context for understanding these concepts.

PREREQUISITES
  • Understanding of forced and damped oscillators
  • Familiarity with the concept of Q-factor in oscillatory systems
  • Knowledge of resonance phenomena in mechanical systems
  • Basic principles of analytical mechanics
NEXT STEPS
  • Research the mathematical relationship between Q-factor and bandwidth in oscillators
  • Study the implications of damping on resonance amplitude
  • Explore the derivation of full-width-half-maximum in forced oscillators
  • Examine case studies of damped harmonic oscillators in practical applications
USEFUL FOR

Students of analytical mechanics, physicists studying oscillatory systems, and engineers involved in mechanical design and vibration analysis will benefit from this discussion.

shanepitts
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Hello,
I have two quick inquiries related to my studies on analytical mechanics.

The first is I don't quite fathom how a full-width-half-maximum of the resonance of a forced and damped oscillator behaves in relation to the Q-factor??

And the second is does the amplitude of a forced and damped harmonic oscillator become infinite at resonance? I know that when the frequency from both the force and damped oscillator are equal the damped oscillator become infinite but they do they both become infinite??

thanks
 
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This came up in a thread a few weeks ago, but this link might be helpful since it contains some of the expressions for the damping and the relationship between bandwidth and Q:

Wikipedia on Q factor.
 

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