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Harmonic motion

  1. Nov 17, 2004 #1
    A spring with spring constant 190 N/m vibrates with an amplitude of 8.0 cm when 0.380 kg hangs from it.
    What is the equation describing this motion as a function of time?
    Assume the mass passes through the equilibrium point, toward positive x (upward), at t = 0.100 s.

    x=A*cos(omega*t + phi)

    I figured out that A is 8.0 cm, and omega is 22.36
    but I can't figure out phi.

    Here's what I did:
    x=0 (because it's at equalibrium at .100 s)
    Plug in numbers and get
    0=A*cos(22.36*.100 + phi)
    0/A = cos(22.36*.100 + phi)
    arcosine(0) = 22.36*.100 + phi
    phi = arcosine(0) - (22.36*.100)

    What am I doing wrong?
  2. jcsd
  3. Nov 17, 2004 #2


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    There are many solutios for [itex]\phi[/tex]. Perhaps you're looking for a particular one? Perhaps you should use the fact that the mass is moving upwards at time [itex]t=0.100[/tex]?
    Last edited: Nov 17, 2004
  4. Nov 17, 2004 #3
    Ah! I got it! Thank you.
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