Express y(t) as a function of x(t)

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Discussion Overview

The discussion revolves around expressing y(t) as a function of x(t) within the context of a homework problem. Participants explore transformations of the function and compare their results with a figure from a textbook.

Discussion Character

  • Homework-related, Technical explanation

Main Points Raised

  • One participant presents a transformation approach leading to the expression y(t) = -0.5x(2t-4)+1.5 and questions discrepancies with a textbook figure.
  • Another participant suggests that the initial answer appears correct.
  • A further participant notes that the time scale for the textbook figure remains unchanged for the interval 4 < t < 5, raising concerns about the validity of the comparison with their plot.
  • Another participant agrees with the correctness of the initial transformation and expression.

Areas of Agreement / Disagreement

While some participants agree on the correctness of the transformation, there is uncertainty regarding the comparison with the textbook figure, indicating that multiple views remain on the interpretation of the results.

Contextual Notes

Participants express concerns about the time scale differences and how they affect the comparison between their plots and the textbook figure, highlighting possible limitations in the problem's setup.

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Homework Statement


Express y(t) as a function of x(t).

https://www.physicsforums.com/attachment.php?attachmentid=61309&d=1378005939

Homework Equations




The Attempt at a Solution


Transformations:
-x(t)
0.5x(t)
x(2t)
x(t-2)
x(t)+1.5

∴y(t) = -0.5x(2t-4)+1.5

Here is the plot:

attachment.png


As seen in the plot above, it is different from the figure in the book (P2.4(b)) on the time interval 4 < t < 5. Where am I going wrong?

Thanks!
 

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It seems that your answer is correct.
 
I just noticed that the time scale for 4 < t < 5 remains the same for the figure in the book. I know the time scale is compressed by 0.5 up until t = 4. So, is the book's figure supposed to look like my plot instead? It seems impossible to express y(t) as a function of x(t) if I use the figure in the book.
 

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