Phase of Simple Harmonic Motion: Determining the Phase at a Specific Time

[sugz]

Homework Statement

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

Homework Equations

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)

 

[berkeman]

Homework Statement

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

Homework Equations

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)

Please show your work. What do you get for x(2)?

 

[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)?

 

[berkeman]

So the phase is equal to 2pi+(pi/3)?

Yes. What is that in radians?

 

[sugz]

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

 

[berkeman]

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

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

 

[sugz]

Now I understand, thank you so much!

 

[berkeman]

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.