# Find the phase difference of two oscilliators given a graph

1. Nov 2, 2016

### Taniaz

1. The problem statement, all variables and given/known data
The two oscillators each have the same mass. Use Fig. 4.1 to determine (i) the phase difference between the two oscillators (picture attached)

2. Relevant equations
Subtracting to find the horizontal shift

3. 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)?

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2. Nov 2, 2016

### 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.

3. Nov 2, 2016

### Taniaz

But they expect us to calculate it rather than approximate it

4. Nov 2, 2016

### Staff: Mentor

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?

5. Nov 2, 2016

### cnh1995

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

6. Nov 2, 2016

### Taniaz

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.
:/

7. Nov 2, 2016

### cnh1995

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.

8. Nov 2, 2016

### Taniaz

You're taking it for the same wave?

9. Nov 2, 2016

### cnh1995

Yes.

10. Nov 2, 2016

### Taniaz

15 divisions?

11. Nov 2, 2016

### cnh1995

Right. So what is the value of one division?

12. Nov 2, 2016

### Taniaz

0.04

13. Nov 2, 2016

### cnh1995

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

14. Nov 2, 2016

### Taniaz

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

15. Nov 2, 2016

### cnh1995

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?

16. Nov 2, 2016

### Taniaz

0.6?

17. Nov 2, 2016

### cnh1995

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

18. Nov 2, 2016

### Taniaz

Is it not 15 div x 0.04 rad/div?

19. Nov 2, 2016

### cnh1995

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?

20. Nov 2, 2016

### Taniaz

I don't understand :/