


 Suppose a particle P rotating anticlockwise with radius A and angular frequency ω.
Of P, the displacement from the center of circle, the tangential velocity (ωA) and the centripetal
acceleration (ω^{2}A) are represented, respectively, by the red, blue, and black vectors in the above figures.
 Suppose the displacement vector makes angle θ = ωt with the positive xaxis, so the projection of this vector on the yaxis is
y = Asinθ = A sin(ωt) ....(1)
 The tangential velocity leads the displacement by π/2, so the projection of the velocity vector on the yaxis is
v_{y} =ωA sin(ωt + π/2) ....(2)
 The centripetal acceleration leads the displacement by π, so the projection of the acceleration vector on the yaxis is
a_{y} =ω^{2}Asin(ωt +π) ....(3)
 Using (1), (2) and the identity sin(θ + π) = sinθ , we obtain a_{y} = ω^{2}y, the SHM equation. Thus, we conclude
 A SHM can be regarded as an axisprojection of a uniform circular motion.
 In shm, the amplitudes of displacement, velocity and acceleration are A, ωA and ω^{2}A respectively.
 Phase Differences: a leads v by π/2 ; v leads displacement by π/2.

