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Simple Harmonic Motion

Kinematics of Simple Harmonic Motion

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Assume a unit circle (a circle with radius=1) with a point on its edge. We wish to find out how fast the angle that is created between that point and the center is changing as the point revolves about the origin.
 
(eg. the angle of a string as we swing it in the vertical circle)
 
speed = distance / time
 
** and in our case: **
 
angular acceleration = distance / time
                                       = 2π / T
 
Where T = period of rotation
             2π = total angular rotation in one oscillation
              ω = angular acceleration
 
And we are left with the formula:
 
ω = (2π)/(period)

---> Trigonometry and Kinematics

Alesa Rabson & Maria Forero - Simple Harmonic Motion