# Simple harmonic motion

The equations of simple harmonic motion can be found by looking at a fixed wheel with radius ${\displaystyle A}$ that is spinning with steady speed ${\displaystyle \omega }$ radians per second. The time ${\displaystyle T}$ taken for one complete turn is ${\displaystyle T=}$ ${\displaystyle 2\pi \over \omega }$ because there are ${\displaystyle 2\pi }$ radians in a full circle.
Imagine a white spot painted on the rim of the wheel. If it starts level with the axle, and the wheel has turned through an angle ${\displaystyle \omega t}$ in time ${\displaystyle t}$ seconds, then the height ${\displaystyle h}$ of the spot above the axle is given by ${\displaystyle h=A\sin \omega t}$ (where ${\displaystyle \sin }$ means the sine of the angle turned, and trigonometry is used to find the height).