NascentOxygen said:
Because the system is so underdamped, the natural frequency is practically equal to the frequency where the response peaks. (Which looks suspiciously co-incident with that 90° crossing on the phase plot, though off-hand I can't say that's right.) I suppose you are approximating this to a second-order system?Loppyfoot said:
NascentOxygen said:
Most likely. Though there is an equation relating frequency at the peak and ζ back to Ѡn if you really wanted to be precise.Loppyfoot said:
The values of Omega and Zeta can be determined by finding the peak frequency and the corresponding phase shift on the magnitude and phase plot. Omega is equal to the peak frequency, while Zeta can be calculated by taking the tangent of the phase shift at the peak frequency.
Finding Omega and Zeta from a magnitude and phase plot allows us to analyze the frequency response and damping characteristics of a system. It also helps in understanding the stability and behavior of the system.
Yes, Omega and Zeta can be calculated using the transfer function of the system. The transfer function can be derived from the differential equations governing the system and then used to calculate the values of Omega and Zeta.
The value of Omega represents the natural frequency of the system, while Zeta represents the damping ratio. A higher value of Zeta indicates a higher damping in the system, which means the system will return to its equilibrium position faster.
Yes, the values of Omega and Zeta can change over time if the system is undergoing any changes. For example, if the system parameters change, the values of Omega and Zeta will also change. In such cases, a new magnitude and phase plot can be generated to determine the updated values of Omega and Zeta.