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Harmonic motion problem

  1. Nov 21, 2004 #1
    I am confused by the following problem. Any help / hints would be greatly appreciated! I understand that the velocity equation is the derivative of the position function... i just don't understand how to derive these first / last equations. :bugeye: THANKS!

    The initial position and initial velocity of an object moving in simple harmonic motion are xi, vi, and ai; the angular frequency of oscillation is (omega).

    a) Show that the position and velocity of the object for all time can be written as:

    x(t) = xi cos(omega * t) + (vi / (omega) )*sin (omega * t)

    v(t) = - xi (omega)sin(omega * t) + vi*cos(omega * t)

    b) If the amplitude of the motion is A, show that

    v^2 - ax = vi^2 - aixi = (omega)^2A^2
  2. jcsd
  3. Nov 22, 2004 #2
    Here's a hint. Consider the substitution of initial conditions in the solutions for displacement and velocity.
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