What does the phase angle phi mean in the harmonic oscillation function?

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Discussion Overview

The discussion revolves around the role of the phase angle phi in the harmonic oscillation function, specifically in the context of simple harmonic motion (SHM). Participants explore its implications for the initial position of the oscillation and the relationship between sine and cosine functions in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the inclusion of the phase angle phi in the function for simple harmonic oscillation, suggesting it may affect the initial position.
  • Another participant asserts that phi determines the initial position of the oscillation and relates it to the cosine function.
  • A different participant raises a question about the derivation of the equation of SHM, specifically regarding the proportionality constant and its relation to the frequency of SHM.
  • Several participants discuss how the graph of SHM would change with different values of phi, with some suggesting it transitions between sine and cosine forms.
  • There is a debate about whether the function starts as sine or cosine and how phi affects this starting point, with one participant emphasizing that phi only shifts the position of the cosine function.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the phase angle phi, particularly regarding its effect on the initial position and the relationship between sine and cosine functions. The discussion remains unresolved with multiple competing perspectives on these points.

Contextual Notes

Some claims about the relationship between sine and cosine functions and their transformations are presented without detailed mathematical justification. The discussion also includes assumptions about the nature of the oscillation function that are not explicitly defined.

CrazyNeutrino
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The function for simple harmonic oscillation is:
Acos(ωT)+\phi
Why is there an angle phi added to the function acos(ωT)?
 
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it's Acos(ωT+ϕ) omega stands for how fast it' s oscilating, but phi determines the initial position( wold be Acosϕ)
 
I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question is , is there any derivation which can show that the constant is the frequency of the shm .
 
If phi had a value, what would the shm graph look like? Or how would it change from Acos(wT)?
 
CrazyNeutrino said:
If phi had a value, what would the shm graph look like? Or how would it change from Acos(wT)?
The graph would change from sine to cosine, (remember, that sin(x+π)=cosx)
 
isnt the function already Acos(wT)+phi?
 
so how could it change from sine if it doesn't start at sine?
 
CrazyNeutrino said:
so how could it change from sine if it doesn't start at sine?
It never started as cosine, it's allways either sine or cosine or somethin in between. It's like you move the cosine a bit to the right and if you move it by π/2 you get sine! SO all phi determines is the initial position!
 
Ok... Thanks! I almost understand.
 

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