1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simple harmonic motion of a body question

  1. Jun 30, 2007 #1
    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.
  2. jcsd
  3. Jun 30, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The phase is simply the argument of the sine function, namely the [itex] \omega t + \frac{\pi}{3} [/itex] That's all there is to it.
  4. Jun 30, 2007 #3


    User Avatar
    Science Advisor
    Gold Member

    I think the "phase of motion" is the argument of the sine function (=ωt+φ)

    So at time t=0, the phase of motion would just be the phase constant (in your problem, π/3). And I think your answer should be between 0 and 2π, so if you compute something larger than 2π, you should subtract multiples of 2π 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...
  5. Jun 30, 2007 #4

    Doc Al

    User Avatar

    Staff: Mentor

    You can trace the SHM motion through [itex]2\pi[/itex] 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 = [itex]\pi/2[/itex]; back to the origin, phase = [itex]\pi[/itex]. Etc.

    Hint: Consider the argument of the sine function.

    (Looks like nrqed and jamesrc both beat me to it!)
  6. Jun 30, 2007 #5
    Thanks for the help. I got it.
    Last edited: Jun 30, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook