Simple harmonic motion facts
In mathematics and physics, when something moves so that its distance from a fixed point (plotted on a graph against time) looks like a sine wave, the movement is called simple harmonic motion. This sort of movement will happen whenever the force towards the fixed point is proportional to the distance from the point and always acts towards that point. Examples include a weight on a spring and a pendulum (approximately).
The amplitude is the biggest distance from the fixed point. The period is the time taken to get back to the same point again (with the same speed and in the same direction).
The equations of simple harmonic motion can be found by looking at a fixed wheel with radius that is spinning with steady speed radians per second. The time taken for one complete turn is because there are 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 in time seconds, then the height of the spot above the axle is given by (where means the sine of the angle turned, and trigonometry is used to find the height).
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The motion of an undamped pendulum approximates to simple harmonic motion if the angle of oscillation is small.