What does phase of the motion in terms of cosine displacement mean?

AI Thread Summary
The discussion centers on understanding the term "phase of the motion in terms of cosine displacement" in the context of simple harmonic motion. The key equation provided is x(t) = A*cos(ωt - φ), where φ represents the phase shift. The phase indicates how far the motion is shifted from a reference point, which is crucial for accurately describing the position over time. The mention of a rotating vector phasor and the unit circle suggests a deeper connection to the cosine function's behavior. Ultimately, the question seeks to clarify the value of φ in the context of the given motion graph.
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What does "phase of the motion in terms of cosine displacement" mean?

I'm getting tripped up on the wording of this homework question.

Homework Statement


Measured acceleration: An accelerometer has measured the simple harmonic motion shown in the image below.

Homework Equations


You want to describe the position as a function of time as a cosine: x(t)=A\cos(\omega t-\phi).
What is the phase of the motion shown in the graph (in terms of a cosine displacement)?
droHh.jpg


The Attempt at a Solution


I've tried reading my textbook for "phase of the motion". There's a section that talks about a rotating vector phasor that references the unit circle. Is this the right path? Are they talking about what the cosine is calculating (i.e. what's inside the brackets of the cosine)?
 
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The phase of a periodic function is the displacement the function has from some predefined 0 point. For example, sin(x) is 90° out of phase from cos(x). The question is just asking for \phi in x(t) = A\cos(\omega t+\phi).
 


Thank you.
 
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