Circular Motion and the Phase Angle of SHM
The angle of rotation q(t) of a body undergoing uniform circular motion is related to the angle wt + f that appears in the sine and cosine functions in Simple Harmonic Motion. This is because circular motion viewed edge on is identical to simple harmonic motion.

Rotation Angle

Phase Angle

Phase Angle in SHM
The complex relationship between an oscillating object's initial phase angle and the angle of rotation of SHM is displayed along with a mass on a spring undergoing SHM.