Simple harmonic can be represented as a projection of circular motion.

If P moves uniformly on a circle as shown in the below figure, then its projection P′ on a diameter of the circle executes SHM.

As the particle P moves on the circle, The position of P′ on the x-axis is given by

x(t) = A cos (ωt + φ)

This is the equation of SHM on the $\times$-axis with amplitude $A$ and angular frequency as $\omega$ Where $A$ is the radius of the circle and $\varphi$ is the angle that the radius OP makes with the $\times$-axis at $t=0$

Similarly, The position of P′ on the y-axis is given by

y(t)=  A sin (ωt + φ)

This is also an SHM of the same amplitude as that of the projection on the x-axis, but differing by a phase of π/2.