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Eqn for SHM, sin function, so why cos?

  1. Dec 20, 2011 #1
    I had thought the eqn of simple harmonic motion is a sinusoidal function of time, with the eqn being:

    x(t) = A sin(wt + ∅0)

    Halfway down this page:
    http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm [Broken]
    in Problems:

    in solution (a) it gives;

    The displacement as a function of time is x(t) = Acos(ωt + φ).

    Why are they using a cos and not a sin function?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 20, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Which one you use is arbitrary. Realize that the only difference between the two is a phase factor. (Shift a sine function by 90° and it becomes a cosine function.)

    Using x = Acosωt just implies that you are starting the clock when the object is at its maximum displacement. Using x = Asinωt implies that you are starting the clock when the object passes the equilibrium point.

    Just two completely equivalent ways of describing the same thing.
  4. Dec 20, 2011 #3
    Thank you Doc Al :smile:
  5. Dec 20, 2011 #4
    Doc Al has said it..... you will not hear a more straightforward explanation
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