Finding Phase Constant and air-track glider

[Liketothink]

Homework Statement

An air-track glider attached to a spring oscillates with a period of 2.3 s. At t=0 s the glider is 3.09 cm left of the equilibrium position and moving to the right at 35.07 cm/s.
What is the phase constant? (in degrees)

Homework Equations

v0x= -wAsin(ro), x=Acos(ro)

The Attempt at a Solution

I divided v0x/x=wtan(ro). I solved for angular speed which was 2.73 rad/s. Now I solved for (ro) by taking tan inverse of (v/-wx). I received 73 as an answer and that's wrong. Would you please help me? Thank you.

 

[talaroue]

Since you are to the left, you have to subtract 180. The anwser you came up with is to the right of the equilibrium point.

 

[Liketothink]

I minus that by 180 so it's 107 but that's still wrong. What do you think is wrong?

 

[dx]

Did you get

r_{0} = \tan^{-1} \frac{35.07}{3.09 \cdot 2.73}?

 

[Liketothink]

yeah, I tried that as well which was 76.4751. Then I minus it from 180 so it's 103.525 but that's wrong.

 

[dx]

Both 76.47 and 76.47 - 180 have the same tangent. You can see by drawing a pic that the one we want is (76.47 - 180).

-103.5 degrees = -1.807 radians.

 

[Liketothink]

is it because it's negative and the distance is negative?

 

[Liketothink]

Also, in this case, is angular speed the same as velocity? If I wanted to find the phase at t=0 s would I just need to use wt+ro, w being the velocity?

 

[dx]

Yes, the cosine of 76.4 is positive, but the initial distance is negative.

 

[Liketothink]

Oh sorry w=2.73. Sorry about that.

 

[dx]

No, angular speed and velocity are different. The angular speed is constant, while the velocity is changing.

v = -Aωsin(ωt + a₀)

 

[Liketothink]

ok, so for t=.5s I get -102.115 but that's wrong. All I did is wt+constant(-103.48). But that's wrong for some reason. Does the constant change at that time?

 

[dx]

Write -103.48 in radians.

 

[Liketothink]

-1.80607 rad

 

[dx]

Do you get the right answer now? (I'm not sure what you're trying to calculate BTW, did you get the correct answer for the phase constant?)

 

[Liketothink]

I got the correct answer for the phase constant but I'm trying the phase for t=.5s. Sorry for the confusion.

 

[dx]

Ok, so at t = 0.5, you have ωt + a₀ = 2.73(0.5) - 1.806. This is in radians. If you want to convert it to degrees, multiply by 360/2pi.

 

[Liketothink]

The question has several parts and it's asking me for the phase at t=.5s. I used the same formula but it's wrong. Could you please let me know what's wrong? thank you.

 

[Liketothink]

Ok thank you very much for all your help. I greatly appreciate it.