Resonant Frequency & Natural Frequency?

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SUMMARY

The discussion centers on the relationship between natural frequency and resonant frequency in control systems. It establishes that when the damping ratio is zero, the resonant frequency equals the natural frequency. Participants emphasize the importance of understanding this relationship, particularly when analyzing transfer functions and constructing root locus plots. Key concepts include the damping ratio, natural frequency, and the use of the Routh-Hurwitz method for stability analysis.

PREREQUISITES
  • Understanding of transfer functions
  • Knowledge of root locus plots
  • Familiarity with damping ratios
  • Proficiency in Routh-Hurwitz stability criterion
NEXT STEPS
  • Research the relationship between natural frequency and resonant frequency
  • Learn how to calculate resonant frequency from damping ratio and natural frequency
  • Explore the concept of ringing frequency in control systems
  • Study advanced techniques for analyzing stability in dynamic systems
USEFUL FOR

Control system engineers, students in engineering disciplines, and anyone involved in system stability analysis and frequency response evaluation.

dominicfhk
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Hello guys! Is it possible to convert a natural frequency to resonant frequency with maybe some kind of formula? I was given a transfer function and I was asked to draw a root locus plot and determine the resonant frequency. I know how to get the damping ratio and natural frequency and the value of K to make the system stable (by using the routh-hurwitz method), but I have no idea how to get the resonant frequency. Thank you so much!
 
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The short answer is "yes" - recall that if the damping ratio is 0, the resonant frequency is the natural frequency: it follows that there is some relationship between the natural frequency, the resonant frequency, and the damping ratio.

You should have notes for these sorts of relationships - like the ringing frequency or the peak frequency.
One of these will be the one you want ;)
 

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