Find the phase difference of two oscilliators given a graph

[Taniaz]

Homework Statement

The two oscillators each have the same mass. Use Fig. 4.1 to determine (i) the phase difference between the two oscillators (picture attached)

Homework Equations

Subtracting to find the horizontal shift

The Attempt at a Solution

I found the two points where both graphs intersect the time axis and took their difference but I am getting a difference of 0.2 (pi) and the mark scheme says 1/3 (pi)?

 

[cnh1995]

Well, I think it is indeed π/3. Compare the phase difference with one half cycle and you'll see that the phase difference is almost 1/3rd of the half cycle i.e. π/3.

 

[Taniaz]

But they expect us to calculate it rather than approximate it

 

[gneill]

But they expect us to calculate it rather than approximate it

I think that @cnh1995 was pointing out that a cursory inspection of the graph seems to support the published answer over yours.

How about you give us more detail for the calculation that you did? Can you point out which intersection points you used, what values you recorded and how you used them to determine the phase angle?

 

[cnh1995]

But they expect us to calculate it rather than approximate it

After doing the exact calculation, the answer is coming out to be pi/3 rad. How many divisions correspond to 180 degree (pi radian)?

 

[Taniaz]

After doing the exact calculation, the answer is coming out to be pi/3 rad. How many divisions correspond to 180 degree (pi radian)?

That's what I'm not sure of. I just took each division as 0.04.

I took the first points where each graph is intersecting the time axis as 0.5 and 0.3 and their difference is 0.2
Similarly I took the next two points of each graph intersecting the time axis which I found to be 1.5 and 1.7.
:/

 

[cnh1995]

I just took each division as 0.04.

How did you decide that?
Look at the thick waveform carefully. Measure the no of divisions between its two successive zero crossings. How many divisions do you get? I am talking divisions in mm and not cm.

 

[Taniaz]

You're taking it for the same wave?

 

[cnh1995]

You're taking it for the same wave?

Yes.

 

[Taniaz]

15 divisions?

 

[cnh1995]

15 divisions?

Right. So what is the value of one division?

 

[Taniaz]

0.04

 

[cnh1995]

0.04

0.04 what? What is the unit? I am asking the value of one division in radian (or degree).

 

[Taniaz]

but it's 0.04 s? How do we get it in radians or degrees?

 

[cnh1995]

but it's 0.04 s? How do we get it in radians or degrees?

Well, since we need the phase "difference", we will ultimetely need an angle. So instead of converting time into radians, I believe it would be convenient to treat the x-axis divisions as rad/mm. You got 15 divisions between two successive zero crossings of the same waveform? So how many radians=15 divisions?

 

[Taniaz]

0.6?

 

[cnh1995]

0.6?

What is the phase difference between two successive zero crossings of the same waveform?

 

[Taniaz]

Is it not 15 div x 0.04 rad/div?

 

[cnh1995]

0.04 rad/div

How did you decide this 0.04 rad/div? Earlier you said it is 0.04s and not 0.04 rad. I think you are confusing the given time scale with radian scale. 0.04s is not equal to 0.04 radian.
What is the phase difference between two successive zero crossings of the same waveform? What fraction of the total waveform does this part represent?

 

[Taniaz]

I don't understand :/

 

[Taniaz]

Is it 180 degrees??

 

[cnh1995]

I don't understand :/

Ok. I think a picture is worth a thousand words.

 

[cnh1995]

Is it 180 degrees??

Right!

 

[Taniaz]

So 15 divisions is 180 degrees then we cross multiply for 5 divisions to find the phase difference of the two waveforms?

 

[Taniaz]

AND we get 60 degrees which is pi/3! Thank you!

 

[cnh1995]

So 15 divisions is 180 degrees then we cross multiply for 5 divisions to find the phase difference of the two waveforms?

Yes.

AND we get 60 degrees which is pi/3! Thank you!

Good!

 

[gneill]

Here's a method that you may find helpful. Lay a piece of paper on your graph so that a straight edge lies along the time axis. Take a pen and mark the significant crossing locations and indicate the known number of radians for the points corresponding to one cycle of one of the waveforms. It looks like the solid waveform is a good choice for this:

Now you have a scale in radians for the waveforms. There's a count of 15 of the graph's minor divisions between $0$ and $\pi$ radians as you've already determined.