Understanding Damped Harmonic Motion Parameters: A Graphing Challenge

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Discussion Overview

The discussion revolves around the parameters of damped harmonic motion, specifically focusing on the undamped natural frequency, damping ratio, and the relationship between TR and r. Participants are seeking confirmation of their calculations and assistance with graphing based on these parameters.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant requests confirmation of their calculations for the undamped natural frequency and damping ratio, as well as assistance with graphing related to these parameters.
  • Another participant corrects the file reference from the first post, indicating that the correct file is provided in their follow-up.
  • A participant points out the relationship between TR and r as given in part D, suggesting that this equation can be used to create the graph.
  • One participant expresses discomfort with a specific calculation involving the ratio $$r = {\omega\over \omega_n}$$ and requests clarification on this expression.

Areas of Agreement / Disagreement

The discussion includes requests for confirmation and clarification, indicating uncertainty about the calculations and the graphing process. No consensus is reached on the correctness of the calculations or the graphing approach.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in their calculations, and there may be dependencies on specific definitions or interpretations of the parameters involved.

matthew1982
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Homework Statement


Hi I have attemted to work out the undamped natural frequency and the damping ratio can someone please confirm if this is correct? and for question d I have worked out r and TR can someone please confirm if this is correct? if all is correct I need help with plotting a graph for question d with the parameters set at the bottom of the question can you please help me anyone?

Homework Equations

The Attempt at a Solution

 

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Hi this is the correct file by the way the file on my first post is incorrect
 

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In part D you are given the relationship between TR and r. You can use that equation to get the graph.
 
Seeing $$r = {\omega\over \omega_n} = r = {10\over 22.4} = 3.565 $$ hurts my eyes (in more than one way). Can you explain this ?
 

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