# Homework Help: Simple harmonic motion of a body question

1. Jun 30, 2007

### srj200

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

A=Ai * sin(wt+ (pi/3)) ,

Where w = pi radians per second, t is in seconds, and Ai = 2.4m.
What is the phase of motion at t = 9.4 seconds? Answer in units of radians.

2. Relevant equations

A is the amplitude.
Ai is the initial amplitude.
w is actually "omega" but I didn't know how to enter that. That is the given angular velocity in rad/s.
Pi is 3.14.....

3. The attempt at a solution
I honesty don't know where to start. I just plugged into the equation with the given data and got

-1.78355 meters.

The answer wants radians. Also, it asks for the "phase of motion". The answer I got is just the final amplitude at the given time.

Any help would be appreciated.
Thanks.

2. Jun 30, 2007

### nrqed

The phase is simply the argument of the sine function, namely the $\omega t + \frac{\pi}{3}$ That's all there is to it.

3. Jun 30, 2007

### jamesrc

I think the "phase of motion" is the argument of the sine function (=&omega;t+&phi;)

So at time t=0, the phase of motion would just be the phase constant (in your problem, &pi;/3). And I think your answer should be between 0 and 2&pi;, so if you compute something larger than 2&pi;, you should subtract multiples of 2&pi; until you are in that range.

E.T.A.: Looks like I was too slow...and Greek letters don't work the way they used to...

4. Jun 30, 2007

### Staff: Mentor

You can trace the SHM motion through $2\pi$ radians of "phase" as the body moves past the origin, goes to maximum + displacement, returns to the origin, goes to maximum - displacement, and then back where it started. When the body crosses the origin, consider its phase to be 0; when it reaches maximum amplitude, phase = $\pi/2$; back to the origin, phase = $\pi$. Etc.

Hint: Consider the argument of the sine function.

(Looks like nrqed and jamesrc both beat me to it!)

5. Jun 30, 2007

### srj200

Thanks for the help. I got it.

Last edited: Jun 30, 2007