Simple Harmonic Motion notes

Simple harmonic motion or SHM does not always seem simple. It describes the regular movement of a point backwards and forwards about a centre where the force and therefore the acceleration is proportional to the distance from the centre. That is a real mouthful, but it is not so complicated as it might sound. For example a ruler twanged on the edge of  a desk vibrates in simple harmonic motion and so do the strings vibrating on a guitar, piano or any other musical instrument.

SHM does not only happen in musical instruments but also in structures, for example a tall building or a bridge wobbling in the wind and vehicles vibrating as the engine runs.

The notes describe and define simple harmonic motion with some care and then extend that explanation using the most common examples. These are of an oscillating spring and of a swinging pendulum (although that is not exactly SHM but very close).

The final two sheets of notes explain the graphs of changes in velocity, acceleration and energy with time.



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