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Oscillary Motion

  1. Nov 11, 2004 #1
    The Problem is:
    A particle executes simple harmonic motion with an amplitude of 2.25 cm. At what position does its speed equal half its maximum speed?

    I've been looking at this for a while, and I cant see how to solve it without more information.

    If I knew the energy and mass I could solve it,
    if I knew the frequency or period I could solve it,
    if I knew the spring constant and mass I could solve it,
    but I dont have any of this, what's the trick?
  2. jcsd
  3. Nov 11, 2004 #2


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    Homework Helper

    HINT: For what value of z does cos z equal half its maximum value?
  4. Nov 11, 2004 #3


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    Use symbols instead of numbers.

    The position of the particle x=Asin(wt), A= 2.25 cm.
    The velocity of the particle v= Awcos(wt).
    The maximum velocity is Aw.
    You look for the position when v=0.5 Aw.
    0.5 Aw = Aw cos(wt) ----> cos(wt)=0.5.

    You only ned to find sin(wt) to get x.

  5. Nov 12, 2004 #4
    You can apply the general velocity formula for SHM here. since maximum velocity is v=rw, then take the half of it and equal to general formula. Work it out and you should be able to find the positions.
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