# Homework Help: Phase of an oscillation

1. Feb 18, 2015

### sugz

1. The problem statement, all variables and given/known data
A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x = 5sin(pi*t + pi/3). The phase (in rad) of the motion at t = 2s is

a) (7pi)/3 b) pi/3 c) pi d) (5pi)/3 e) 2pi

2. Relevant equations

3. The attempt at a solution
I plugged in the value for t=2 but I really did not know how to past this point. The answer is supposed to be a)

2. Feb 18, 2015

### Staff: Mentor

3. Feb 18, 2015

### sugz

x(2) = 4.33. But how do I determine the phase? Is the phase simply what is in the brackets? So the phase is equal to 2pi+(pi/3)?

4. Feb 18, 2015

### Staff: Mentor

Yes. What is that in radians?

5. Feb 18, 2015

### sugz

Its 7pi/3. So for any equation of a particle in SHM, the phase is the part inside the brackets?

6. Feb 18, 2015

### Staff: Mentor

Sort of. For a sinusoidal function (sin or cos), you can picture the value in 2-dimensions on a circle. The amplitude is the radius of the circle, and the point that rotates around the circle with time has some phase angle θ with the positive horizontal axis. If you have a sin() function like you do in this problem, then yes, the value in the () is the phase angle θ with the horizontal axis.

http://images.tutorcircle.com/cms/images/106/unit-circle-example.png

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7. Feb 18, 2015

### sugz

Now I understand, thank you so much!

8. Feb 18, 2015

### Staff: Mentor

It may be true in general, but sometimes we define phase with respect to something, so I'm not sure it is a general statement. Others can correct that if appropriate.