When you project a circular motion in a horizontal plane onto a vertical plane, it's like seeing a simple harmonic motion in action. Imagine a hula hoop spinning horizontally and its shadow cast on a wall. That shadow moves like a simple harmonic motion!

Think of a car going round a roundabout. If we take a birds-eye view (from top), we'd see circular motion. But if there's a light above casting a shadow on a wall, the car's shadow would move back and forth like a pendulum!

• θ: Phase angle, the angle between arrow and x-axis.
• ω: Angular speed, how fast something rotates.
• r: Radius of circle.

• x  = rcosθ = & ⁡y = r sin θ
• x =x₀​cosωt - Begins at extremes
• x =x_0​sinωt - Begins in centre
• v = ωx₀​cosωt - Velocity
• a = − ω²x - Acceleration

• Displacement-time graph: Looks like a wave (sine curve).
• Velocity-time graph: Still wavy but a different pattern (cosine curve).
• Acceleration-time graph: Wave turned upside down (negative sine curve).

🧐 Did you know? If you slide down a velocity-time graph's slope, you'll get acceleration. Slide down the displacement-time graph's slope? Boom, you've got velocity.