How Do I Know the Following Equations is Dimensionally Correct?

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Homework Help Overview

The problem involves determining the dimensional correctness of the equation y=2 cm * cos(k*x), where k=2 m^-1. Participants are questioning the dimensions of the variables involved, particularly what x and y represent in a physical context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are exploring the dimensions of y and questioning the meaning of x. There is discussion about whether x could represent an angle or arc length, and how k relates to these dimensions.

Discussion Status

The discussion is ongoing, with participants raising questions about the definitions and dimensions of the variables. Some guidance is being offered regarding the nature of the variables, but no consensus has been reached on their specific meanings.

Contextual Notes

There is a lack of information regarding the definitions of x and y, which is central to understanding the dimensional correctness of the equation. Participants are also considering the implications of using radians in the context of the cosine function.

JustSomeGuy80
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Homework Statement


The problem asks to choose the dimensionally correct equation. In the back of the book it says that the correct answer is y=2 cm * cos(k*x), where k=2 m^-1. What do x and y stand for? The book doesn't say. Does each variable usually represent a certain dimension in physics? From my understanding, dimension y should be the same as dimension ( 2 cm * cos(k*x) ). But what is y?


Homework Equations





The Attempt at a Solution

 
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If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?
 
Appears to be dealing with harmonics. Notably spring harmonics. If so 'y' would be vertical or horizontal displacement.
 
rock.freak667 said:
If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?

an angle? arc length?
 
JustSomeGuy80 said:
an angle? arc length?

kx should give radians if k is m-1, x would be?
 

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