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Homework Help: Simple Harmonic Motion Displacement

  1. Apr 19, 2014 #1


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    1. The problem statement, all variables and given/known data
    A particle is in simple harmonic motion with period T and with position as a function of time given by x(t) = A cos(wt+ø).

    At time t = 0 the particle is at x = A/2 with positive velocity. The next time it is at the same position is ___?

    2. Relevant equations


    3. The attempt at a solution

    So I know the cosine of the argument has to = 1/2 for the position to be half the amplitude. The first time this happens is at t = 0. This implies the phase constant ø is pi/3.

    The next time the cosine argument is a positive 1/2 is when the argument equals 300 degrees. Therefore:

    wt + pi/3 = 5pi/3
    wt = 4pi/3
    t = 4pi/(3w)

    w = 2pi/T

    t = 4pi/[3(2pi/T] = 4pi/[6pi/T] = 2T/3.

    The answer however is t = T/3.
  2. jcsd
  3. Apr 20, 2014 #2


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    If the particle has positive velocity at t =0 zero, doesn't ωt+ø have to be -π/3 (-60°) ?
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