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Very easy simple harmonic motion question that I keep getting wrong

  1. Apr 7, 2012 #1
    1. The problem statement, all variables and given/known data

    In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds.

    x = (7.00 cm) cos(4t + π/6)

    At t = 0, what is its velocity?

    2. Relevant equations

    v(t) = -A sin(ωt + ϕ)

    3. The attempt at a solution

    It first asked me to find the position so I did that easily by plugging in for time and getting an answer. And to get velocity I just had to take the derivative of the initial function and then plug in once again. However, when I do this I do not get the correct answer and I can't figure out why.

    The expression should read

    v(t) = -7.00 cm sin (4(0) + π/6)

    This basicaly breaks down to -7.00 * 1/2 right?

    When I do this I get -3.5 cm/s and it says my answer is off by more than 10%. No idea what I am doing wrong.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 7, 2012 #2

    cepheid

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    Staff Emeritus
    Science Advisor
    Gold Member

    The expression in red above is not correct. It should be:

    v(t) = -Aωsin(ωt + ϕ)

    Since you know how to take a derivative, you can verify this for yourself. You can also see that the units work out in this case. The amplitude of the velocity has to have units of cm/s, not just cm.
     
  4. Apr 7, 2012 #3

    gneill

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    Staff: Mentor

    Check your derivative carefully. While d/dt cos(t) = -sin(t), d/dt cos(ωt) ≠ -sin(ωt)...
     
  5. Apr 7, 2012 #4
    Ah ok I was forgetting to multiply my Amplitude by ω

    Got it thanks
     
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