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Understanding System Responses: Analysis of Underdamped and Critically Damped Systems

This document provides an in-depth exploration of system responses, focusing on first and second-order systems. It discusses key characteristics such as over-damped, critically damped, and underdamped system responses. Highlighted examples include a specific underdamped response with a decay ratio of 0.043, rise time of approximately 1, settling time of 5, and an overshoot of about 20.8%. Additionally, it investigates various damping ratios (ζ), particularly 0.4472 and 0.2154, and their influence on system behavior.

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Understanding System Responses: Analysis of Underdamped and Critically Damped Systems

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  1. CBE / MET 433 13 Feb 12

  2. System Responses: 1st Order: 2nd Order:

  3. System Responses:

  4. System Responses:

  5. System Responses: Over/Critically Damped

  6. System Responses: Example

  7. System Responses: Underdamped

  8. System Responses: Underdamped T = 3.142 Decay Ratio = 0.043 Rise Time ~ 1 Settling Time = 5 Overshoot ~ 20.8%

  9. System Responses: Underdamped = 0.4472 = 0.2154

  10. System Responses: Underdamped

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