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Stuck on harmonic motion question

  1. Apr 22, 2005 #1

    I've been stuck on trying to figure out what im not seeing in the problem as i just cant seem to get the answer.

    A particle moving in simple harmonic motion with a period T = 1.5s passes through the equilibrium point at time t initial = 0 with a velocity of 1.0m/s to the right. At a time t later, the particle is observed to move to the left with a velocity of 0.50m/s. What is the smallest value of the time t?

    I just cant see what to do :mad: (although i have calculated the angular frequency ( 4(pi)/3).

    Thanks in advance.
  2. jcsd
  3. Apr 22, 2005 #2

    Andrew Mason

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    The position of the particle will be:

    [tex]x = A_0sin(\omega t + \phi)[/tex]

    Given the initial condition, x = 0 at t = 0, [itex]\phi = 0[/itex]

    The speed is given by:

    [tex]\dot x = -A_0\omega cos(\omega t) = v_0cos(\omega t)[/tex]

    If [itex]\dot x(t_1) = v_1 = -.5v_0[/itex], then what is [itex]cos(\omega t_1)[/itex]?

    So from that, you should be able to work out t1.

  4. Apr 22, 2005 #3
    ahh, i had tried that but i differetiated wrong got the answer now thanks.
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