Phase constant sign (quick question)?

In summary, the phase constant for the given graph is either 60 degrees or -60 degrees, as the cosine function is many-to-one. To determine the correct value, one must consider other factors, such as the given amplitude and frequency.
  • #1
tyrostoken
4
0

Homework Statement


A = 20 cm
14.EX05.jpg

Given the graph, what is the phase constant(in degrees)?
(I have already solved for amplitude and frequency)

Homework Equations


x(t) = A cos (wt + ϕ)

The Attempt at a Solution


x(t) = A cos (wt + ϕ)
Taking from t = 0, we find:
10 = 20cos(w*0 + ϕ)
10 = 20cos(ϕ)
1/2 = cos(ϕ)
cos-1(1/2) = ϕ
ϕ = 60 degrees.

I tried submitting the answer and it said check signs, so I entered -60 degrees.
Why is this answer negative?
 
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  • #2
Hi tyrostoken, Welcome to Physics Forums!

The cosine trig function is many-to-one: Note that cos(Φ) = cos(-Φ). So when you solved for Φ the answer might have been either +60° or -60°. It's up to you to check which one fulfills the given conditions.
 
  • #3
To add to gneill's answer...
Imagine shifting the curve left until the value at t=0 is once again 0.5. This solves your equation, but the graph is visibly different. So you need another fact about the graph to fix the phase. What obvious difference is there in the graphs?
 

Related to Phase constant sign (quick question)?

What is phase constant sign?

The phase constant sign refers to the mathematical sign associated with the phase constant in a sinusoidal function. It can be either positive or negative, depending on the specific equation and its parameters.

How is the phase constant sign determined?

The phase constant sign is determined by the position of the graph relative to the x-axis. If the graph is above the x-axis, the phase constant sign is positive. If the graph is below the x-axis, the phase constant sign is negative.

What is the significance of the phase constant sign?

The phase constant sign plays a crucial role in determining the phase shift of a sinusoidal function. It helps in identifying the starting point of the function and how it will be shifted along the x-axis.

Can the phase constant sign be changed?

Yes, the phase constant sign can be changed by manipulating the parameters of the sinusoidal function. For example, adding a constant term to the function will change the phase constant sign.

What happens if the phase constant sign is ignored?

If the phase constant sign is ignored, it can lead to incorrect interpretations of the sinusoidal function. This can result in errors in calculations and predictions, leading to inaccurate conclusions.

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