Oscillator Problem: Find Phase Constant

[lostinphysics44]

Homework Statement

An air-track glider attached to a spring oscillates with a period of 1.50 s. At t=0s the glider is 4.50 cm left of the equilibrium position and moving to the right at 32.6 cm/s.find the phase constant.

Homework Equations

w=2pi/t=2pi/1.5=4.189
x=Acos(wt+phi)
v=-awsin(wt+phi)

The Attempt at a Solution

i tried a systems of equations approach with time equals 0, so the w part drops out, and i keep getting the wrong answer. is this the right approach?

 

[learningphysics]

What did you get for a and phi?

 

[lostinphysics44]

i plugged in and got 32.9=-4.189(4.5/cos(phi))(sin(phi)) and phi=-1.049, which was incorrect

 

[lostinphysics44]

i plugged in and got 32.9=-4.189(4.5/cos(phi))(sin(phi)) and phi=-1.049, which was incorrect

sorry should say 32.6, but either way it is still wrong

 

[rootX]

I get 1.5535, is that correct?

 

[rootX]

i dun have any 4.5 in my equation though

 

[Irid]

Your answer seems correct to me. Maybe the equation for motion is

$$x=A \sin \omega t$$

instead. Then $$\Delta \phi = 0.522$$. All is a matter of convention.

 

[lostinphysics44]

i dun have any 4.5 in my equation though

no that is wrong too, i only have 2 chances left to get this right.

 

[rootX]

I simply used this eq:
d = (a).sin(m[t] + p)
v = (a.m).cos(m[t]+p)

and didn't give consideration to the signs

 

[Irid]

Also you may consider the fact that the glider is in the right, and moving to the left, so velocity might be negative, but it depends on axis orientation.

 

[rootX]

oops, I used 450 for 4.5
so now i get phi = 0.5242

 

[lostinphysics44]

I simply used this eq:
d = (a).sin(m[t] + p)
v = (a.m).cos(m[t]+p)

and didn't give consideration to the signs

i used the same equations but the one i received has cosine in the distance formula and sine in the velocity since velocity is the derivative of the distance function

 

[lostinphysics44]

.52 is also incorrect

 

[learningphysics]

sorry should say 32.6, but either way it is still wrong

You should have used -4.5 in your calculation...

 

[learningphysics]

Do they want the phase in degrees?

 

[rootX]

wait for someone else, I will try to find the mistake.

maybe, that's why! lol

 

[lostinphysics44]

Do they want the phase in degrees?

no radians in the range:

-pi rad < phi < pi rad

 

[rootX]

You should have used -4.5 in your calculation...

I think that's the only option left,
but why its -4.5?

yes, because d(cos t) dt = -sin t~!~! :D

mine weren't correct because that value was for sine functions.

 

[learningphysics]

OK... I'm getting phi = 1.0465 and A = -8.98966

Are you sure the distance is in the form of Acos(wt + phi) and not Asin(wt + phi) ?

 

[rootX]

yes, I also got that too for phi

 

[learningphysics]

yes, I also got that too for phi

Cool. :) Is the A supposed to be in cm or m... be careful about that before you plug in the answer...

 

[lostinphysics44]

OK... I'm getting phi = 1.0465 and A = -8.98966

Are you sure the distance is in the form of Acos(wt + phi) and not Asin(wt + phi) ?

yes i am sure of the formulas, and i already tried that answer for phi and it was marked as incorrect

 

[learningphysics]

yes i am sure of the formulas, and i already tried that answer for phi and it was marked as incorrect

Did you try -1.049 or 1.046555? You wrote -1.049 in the thread earlier which is wrong...

 

[lostinphysics44]

i tried both

 

[lostinphysics44]

dont worry about it i'll figure it out tomorrow from the professor

 

[rootX]

...:shy:...

please post the correct solution tomm
thnx.

 

[learningphysics]

Ok. anyway here's another answer I get:

pi = -2.095
A = 8.98999

you might have already tried it.

 

[learningphysics]

did they also say A > 0?