SHM as a projection of circular motion :

Let a particle be moving uniformly on a circle of radius A with angular speed ω.

If at t = 0, particle starts its motion from x-axis and in time t , it goes to p , then we have

x = OQ = A Cosθ = A Cosωt

y = OR = A Sinθ = A Sinωt

where Q and R feet of the perpendiculars drawn from P on diameter along the X-axis and the Y-axis respectively

From above equation it can be said that Q and R performing SHM about O along the x-axis and the Y-axis respectively with the same angular speed ω.

From figure (b) centripetal acceleration of the particle at P is Aω^{2}.

Resolving this acceleration along PR and PQ

a_{R} = ω^{2}Asinωt = ω^{2}x

a_{Q} = ω^{2}Acosωt = ω^{2}y

The direction of a_{R} is opposite to X and the direction a_{Q} is opposite to Y.

Therefore, also from acceleration point of view, it can be said that Q and R are performing SHM.

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