swatikiss
Nov21-04, 09:15 PM
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
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