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

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SUMMARY

The discussion centers on understanding the "phase of the motion in terms of cosine displacement" in the context of simple harmonic motion. The equation provided, x(t) = A cos(ωt - φ), illustrates that φ represents the phase shift of the motion. The phase shift indicates how far the cosine function is displaced from its standard position, with specific reference to the relationship between sine and cosine functions, where sin(x) is 90° out of phase with cos(x). The key takeaway is that the question is asking for the value of φ in the cosine equation.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with trigonometric functions, specifically cosine and sine
  • Knowledge of phase shifts in periodic functions
  • Ability to interpret equations of motion in physics
NEXT STEPS
  • Study the concept of phase shifts in trigonometric functions
  • Learn about the unit circle and its application to harmonic motion
  • Explore the relationship between sine and cosine functions in detail
  • Investigate the use of phasors in analyzing periodic motion
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Students studying physics, particularly those focusing on mechanics and wave motion, as well as educators seeking to clarify concepts related to simple harmonic motion and phase relationships in trigonometric functions.

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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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