The figure shows a flat circular disc rotating with uniform speed in the vertical plane about a horizontal axis passing through its center. A parallel beam of light is made to fall on the disc. A peg 'Q' on the rim of the disc executes uniform circular motion casting a shadow on the screen. This shadow 'P' of the peg is observed on a vertical plane. This shadow is found to execute SHM, with its mean position at the mid point of the line described.
The above figure shows a body moving with uniform speed along a circle. Let perpendiculars be drawn from different positions of the body onto any diameter, say the vertical diameter. Let T represent the time taken by the body to complete one revolution. This can be divided into eight equal intervals namely 
and so on.
When the body moves from B to C, the foot of the perpendicular moves from P1 to P2. It is seen from the figure that P2 coincides with C. When the body moves from C to D, the foot of the perpendicular moves from P2 to P3. It is seen from the figure that P3 coincides with P1. The displacements of the foot of the perpendicular are represented in the adjacent graph. The curve resembles a sine curve.
From the above discussion, it follows that SHM can have an alternative definition as -“when a particle executes uniform circular motion, the foot of the perpendicular drawn from the particle on any diameter of the circle, executes SHM”. In other words, SHM is the projection of uniform circular motion on the diameter. The circle in the above case is called the circle of reference.