Phase Constant and glider

Rest is a good idea!In summary, the air-track glider attached to a spring oscillates with a period of 1.5s and starts at 5.0 cm left of equilibrium position with a velocity of 36.3 cm/s to the right. To find the phase constant, the equations x = Acos(\varpit + \phi 0) and Vx = -Vmax(\varpit + \phi 0) can be used together. By solving for \phi 0, a value of -60 degrees or pi/3 is obtained. However, since inverse trig functions only give one of two possible answers, it must be determined if the answer is 60 degrees or 180 degrees away
  • #1
BioCore

Homework Statement


An air-track glider attached to a spring oscillates with a period of 1.5s. At t = 0s the glider is 5.0 cm left of the equilibrium position and moving to the right at 36.3 cm/s.

What is the phase constant, [tex]\Phi[/tex]0?


Homework Equations



x = Acos ([tex]\varpi[/tex]t + [tex]\phi[/tex] 0) {1}

Vx = -Vmax ([tex]\varpi[/tex]t + [tex]\phi[/tex] 0) {2}

The Attempt at a Solution


I tried to rearrange equation two for the phase constant, but I am missing A (amplitude). I have tried using vmax = [tex]\varpi[/tex] A but that only works with maximum velocity which I do not have. Maybe I am not seeing something clearly. Can anyone help me out please?
 
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  • #2
Hi BioCore,

BioCore said:

Homework Statement


An air-track glider attached to a spring oscillates with a period of 1.5s. At t = 0s the glider is 5.0 cm left of the equilibrium position and moving to the right at 36.3 cm/s.

What is the phase constant, [tex]\Phi[/tex]0?


Homework Equations



x = Acos ([tex]\varpi[/tex]t + [tex]\phi[/tex] 0) {1}

Vx = -Vmax ([tex]\varpi[/tex]t + [tex]\phi[/tex] 0) {2}

This equation is missing the trig function. Is that just a typo?

The Attempt at a Solution


I tried to rearrange equation two for the phase constant, but I am missing A (amplitude). I have tried using vmax = [tex]\varpi[/tex] A but that only works with maximum velocity which I do not have.
They did not give a numerical value for [itex]v_{\rm max}[/itex], but it's in the equation you need to work with, so by using that relationship you can eliminate one of the unknowns from your two equations.

You'll find the answer by solving the x and v equations together. Based on what the problem gives you, how can you do that to find [itex]\phi[/itex]?
 
  • #3
Yes sorry it was a typo. Ok so when I solved the formula's together I get:

[tex]\phi[/tex] 0 = tan-1 ([tex]\frac{Vx }{-\varpi x}[/tex])

Which when I solve for I get -60 degrees or pi/3. Now the answer they got is -2pi/3 or -120 degrees.

I can't seem to explain to myself how to it is -120 degrees although I think I know why they say that.
 
  • #4
BioCore said:
Yes sorry it was a typo. Ok so when I solved the formula's together I get:

[tex]\phi[/tex] 0 = tan-1 ([tex]\frac{Vx }{-\varpi x}[/tex])

Which when I solve for I get -60 degrees or pi/3. Now the answer they got is -2pi/3 or -120 degrees.

I can't seem to explain to myself how to it is -120 degrees although I think I know why they say that.

When you find an inverse trig function with a calculator, you only get one of the two possible answers. So when you get your answers of 60 degrees (your post said -60 but you meant 60, right?) you'll actually need to determine if the answer is 60 degrees or 180 degrees away from that, which would be the -120 degrees.

There are several ways to find out, but probably the quickest way is to see which one solves the original equations you wrote down (for x and v) with the data you got from the problem.
 
  • #5
alphysicist said:
When you find an inverse trig function with a calculator, you only get one of the two possible answers. So when you get your answers of 60 degrees (your post said -60 but you meant 60, right?) you'll actually need to determine if the answer is 60 degrees or 180 degrees away from that, which would be the -120 degrees.

There are several ways to find out, but probably the quickest way is to see which one solves the original equations you wrote down (for x and v) with the data you got from the problem.

Yeah sorry I meant +60 degrees, I am just very tired right now and I think I will go get some rest. But thanks a lot for the help and understanding the answer. Appreciate it a lot.
 
  • #6
Sure, glad to help!
 

1. What is the phase constant?

The phase constant, denoted as φ, is a measure of the position of a sinusoidal wave at a given point in time. It represents the initial phase angle of the wave, or the starting point of the wave on the x-axis.

2. How is the phase constant related to the glider?

In the context of a glider, the phase constant is used to describe the position of the glider on its trajectory. It is directly linked to the glider's displacement, velocity, and acceleration at any given time.

3. Can the phase constant change over time?

Yes, the phase constant can change as the glider's position changes. As the glider moves along its trajectory, the phase constant will shift accordingly to reflect the new starting point of the wave.

4. How is the phase constant calculated?

The phase constant can be calculated by determining the initial position of the glider, measuring the wavelength of the wave, and using the equation φ = 2πx / λ, where x is the initial position and λ is the wavelength.

5. What is the significance of the phase constant in glider experiments?

The phase constant is an important parameter in glider experiments as it helps to describe the motion of the glider and its relationship to the wave. It can also be used to calculate other important variables, such as the frequency and period of the wave.

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