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. THANKS!(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Homework Help: Harmonic motion problem

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