Another Trig question (sine wave)

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Homework Help Overview

The discussion revolves around a trigonometric function modeling the swaying motion of a tall building, specifically focusing on the interpretation of the amplitude of the sine wave based on the problem's wording.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive the equation of motion based on the given parameters but questions whether the stated sway of 100 cm refers to the amplitude or the total distance swayed. Participants explore the implications of the wording in the problem.

Discussion Status

Participants are actively engaging in clarifying the interpretation of the problem's wording. Some have offered insights regarding the correct interpretation of the amplitude, suggesting that the 100 cm refers to the radius of the sway, while others have provided reasoning to support this view. The discussion is constructive, with no explicit consensus reached but productive insights shared.

Contextual Notes

The original poster expresses uncertainty about the interpretation of the problem's wording, which may affect the formulation of the sine function. The discussion reflects on the potential ambiguity in the terms used in the question.

Imperil
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During a strong wind, a tall building, such as the CN Tower, can sway back and forth as much as 100 cm, with a period of 10s.

b) Write an equation for this function, in the form y = a sin kx

My answer:

2Pi / k = 10
10k = 2Pi
k = Pi/5

y = 100sin(Pi/5)x

Now my question is regarding the wording of the question. It says that it can sway back and forth as much as 100 cm but does not state if that is the diameter or radius. Am I correct in thinking it is referring to the radius?

Or would the correct answer be: y = 50sin(Pi/5)x because it swings 50 cm each way? Sorry to ask such a stupid question I'm just not 100% sure what it is asking.
 
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I'm pretty sure they mean 100cm is the 'radius' (properly called the amplitude of vibration).
 
Specifically, because of the wording "back and forth", I agree with dx. 100 cm "back" and 100 cm "forth" is 100 cm in each direction. If it had simply said "sways 100 cm" then I would think "50 cm in each direction".

(I actually started to disagree with dx, then reread the statement!)
 
Great thanks so much for the help guys I really appreciate it :)
 

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