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Simple Harmonic Oscillator

  1. Apr 11, 2008 #1
    [SOLVED] Simple Harmonic Oscillator

    1. The problem statement, all variables and given/known data
    The equation of motion of a simple harmonic oscillator is (second derivative of x wrt t) d2x/dt2 = -9x, where x is displacement and t is time. The period of oscillation is?


    2. Relevant equations
    2 pi f = omega
    f = 1/T



    3. The attempt at a solution
    Given the relevant equations, one can show that
    omega / 2pi = f
    2pi/omega = T

    The answer is 2pi/3 by the way, and I have trouble getting to this number. I probably have to integrate something, but I don't know what that would buy me. dx/dt = -9/2 x^2 and x = -3/2 x^3. When x is sinusoidal, I know the general form of the equation, but I am totally lost here.
     
  2. jcsd
  3. Apr 11, 2008 #2
    The sine will go away when you cancel.

    x = A sin omega t
    v = dx/dt = A omega cos omega t
    a = dv/dt = d2x/dt2 = -A omega^2 sin omega t

    The problem given: d2x/dt2 = -9x
    becomes: -A omega^2 sin omega t = -9 (A sin omega t)

    everything cancels except: - omega^2 = -9
    omega = 3

    omega = 2 pi f = 2 pi / T
    3 = 2 pi / T

    T = 2 pi / 3
     
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