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Homework Help: Mass oscillating on spring

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data

    The position of a mass that is oscillating on a spring is given by x(t) = (14.5cm)cos[(14.0s-1)t].
    What is the speed of the mass when t = 0.820 s?

    2. Relevant equations

    A= Amplitude
    W= Angular frequency

    x(t) = ACos(Wt)
    v(t) = -WASin(Wt)

    3. The attempt at a solution

    v(0.820) = (-14.0)(14.5)Sin[(14.0)(0.820)]
    = (-203)Sin[11.48]
    = -40.4 cm/s

    This seems so easy and yet apparently I have the wrong answer... any insight? :/ Thanks in advance
  2. jcsd
  3. Dec 3, 2008 #2


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    Gold Member

    What you did seems right to me.
  4. Dec 3, 2008 #3
    Check the units of your frequency. It looks like you have the value in Hertz (or oscillations per second); try converting the instances of frequency to radians per second (and if you're carrying out the sine calculation on a calculator then change the mode to radians instead of degrees).
  5. Dec 3, 2008 #4
    Okay, that makes more sense...

    W=2 x pi x freq

    thus v(t) = -(2 pi 14)(14.5)Sin[(2 pi 14)(0.82)]

    which gives -160 cm/s (with 3 sig figs)... but it still isn't right.
    I suppose there shouldn't be a negative should there? Since speed is scalar... but 160 isn't the right answer either. :/
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