Why is the time interval T/4 - t, not T/4 + t, in damped oscillation?

[Carbon123]

Homework Statement

So In the following picture is the problem and its solution (Problem 130)

Homework Equations

KE =1/2 m v2 x:=w^2x

The Attempt at a Solution

I am confused of the fact that the time from the spring touching t₂ is T/4-t where T is the period oscillations while t is the time to reach equillibrium position.Is it not supposed to be the sum ? Another one is the final work energy statement , why would there be x₃² is it not supposed to be x2 ?
Thanks in advance.

 

[kuruman]

I cannot read your pictures, so at least I will not be able to assist you. Perhaps you might consider re-posting clearer ones?

 

[Carbon123]

The picture is a screenshot from a pdf file.Do you have any suggestion on how I can upload a clear one ? (The screenshot is crystal clear)

 

[kuruman]

I suggest that you first read (or reread) the guidelines for users and helpers.
https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/
Then, instead of posting the contents of 3 pdf files, try to summarize and type in the part(s) of the problem that is (are) relevant to your question. Put yourself in the place of the reader and make sure all the relevant information is conveyed and nothing more.