SHM as a Circular Projection

• A point moves around a circle at constant angular speed. Its shadow on one diameter moves left and right.
• The circle radius becomes the amplitude of the shadow. One complete rotation becomes one complete oscillation.

1. Resolve the radius onto the screen.
   $$x=R\sin\theta$$
2. For steady circular motion:
   $$\theta=\omega t$$
3. Substitute:
   $$x=R\sin(\omega t)$$

A recent Paper 4 question used this projection directly (9702/41/O/N/25 Q1(c)).