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Simple harmonic motion and amplitude

  1. Jul 22, 2004 #1
    I have a short question:

    an object undergoes simple harmonic motion with a period T and amplitude A. How long does it take the object to travel from x = A to x = A/2 ?

    the answer is T/6, but im not sure how to get to that,

    Do I get it from x = Acos(2pi/T xt)?
    help :cry:
     
  2. jcsd
  3. Jul 22, 2004 #2

    jamesrc

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    Gold Member

    You could (but I wouldn't use an x to stand for multiplication especially in an equation that already has an x in it). You could solve for t when x = A and when x = A/2 and find the difference in times.

    You know that x = A at t = 0.

    for x = A/2:

    [tex] x = \frac A 2 = A\cos \left( \frac{2\pi t}{T} \right ) [/tex]

    The cosine of 60 degrees is 1/2, so this reduces to:

    [tex] \frac \pi 3 = \frac{2\pi t}{T} [/tex]

    Solve for t and you'll find the answer.
     
  4. Jul 22, 2004 #3
    thanks so much :smile:
     
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