Physics · PUBLIC INTERACTIVE LESSON

Simple Harmonic Motion — The Shadow of Circular Motion

Follow a rotating point, its shadow, and a displacement graph. Discover the connection that makes harmonic motion click.

WHAT YOU WILL DISCOVER

Connect circular motion with oscillation
Investigate amplitude, frequency and phase
Read displacement, velocity and acceleration

PHYSICS LAB01 / CIRCULAR MOTION

A circle. A shadow. A wave.

One motion, three ways to see it.

x = A \cos (ω t + φ)

t = 0.0 s · x = 1.00 m

Amplitude A1.0 mAngular frequency ω1.0 rad/sInitial phase φ0°

Velocity0.00 m/s

v = - A ω \sin (ω t + φ)

Acceleration-1.00 m/s²

a = - ω^{2} x

Period6.28 s

T = \frac{2 π}{ω}

GUIDED EXPLORATION · 1 / 5

Observe the blue point moving counterclockwise at constant angular speed.

Why does the shadow perform SHM?

The horizontal component of a radius A is A cos θ. Uniform rotation gives θ = ωt + φ, so x = A cos(ωt + φ). Differentiating once gives velocity; twice gives a = −ω²x. Acceleration is proportional to displacement and always points towards equilibrium.

Common misconception: the rotating point has constant speed, but its projection does not. Changing playback speed changes how quickly you view the simulation, not its physical parameters. The graph recomputes the current experiment when a parameter changes.

A: amplitude (metres); ω: angular frequency (radians per second); φ: initial phase (radians); t: simulation time (seconds).

Download the learning summary ↓

At which position is the projection moving fastest?

Double ω while keeping A fixed. What happens to the period?

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Where will your curiosity take you next?

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