Simple harmonic motion - vibration frequency

  1. I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
  2. jcsd
  3. Andrew Mason

    Andrew Mason 6,959
    Science Advisor
    Homework Helper

    The equation of motion is:

    [tex]F = ma = m\ddot{x} = -kx[/tex]

    The general solution is:

    [tex]x = A_0\sin(\omega t + \phi)[/tex] where [itex]\omega^2 = k/m[/tex]

    [itex]A_0[/itex] is the maximum amplitude of vibration (maximum x). The maximum acceleration occurs when x = ? What is the acceleration at that point? (hint: use the equation of motion to find maximum value for a).

    From that you should be able to determine [itex]\omega[/itex]

    Last edited: Oct 18, 2010
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