Matching Initial Position and Velocity of Oscillator

  1. 1. Find C and S in terms of the initial position and velocity of the oscillator.
    Give your answers in terms of x_0, v_0, and omega. Separate your answers with a comma.




    2. x(t) = X_0 + v_0*t + 0.5at^2
    x(t) = C*cos(omega*t) + S*sin(omega*t)




    3. Taking the derivative of x(t):

    v(t) = -C*omega*sin(omega*t) + S*omega*sin(omega*t)

    Thus,

    x_0 = C
    v_0 = S*omega

    How don't quite see how to solve for C and S in terms of x_0, v_0, and omega only.
     
  2. jcsd
  3. This is as good as I've gotten it:

    C = [x_0 + v_0*t + 0.5at^2] / cos(omega*t)

    S = [x_0(1-cos(omega*t)) + v_0*t + 0.5at^2] / sin(omega*t)
     
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