Understanding Damped Harmonic Motion Parameters: A Graphing Challenge

[matthew1982]

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

 

[matthew1982]

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

 

[donpacino]

In part D you are given the relationship between TR and r. You can use that equation to get the graph.

 

[BvU]

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 ?