# Why is simple harmonic motion called so?

Is the motion of a simple pendulum, a simple harmonic motion? It stops vibrating after sometime.

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$y(\theta) = A\sin \theta+ B \cos \theta$ is known as the simple harmonic function. All the motions which can be represented by this function are known as simple harmonic motions.

Motion of a simple pendulum is approximately a simple harmonic motion for small amplitudes. It stops vibrating after some-time due to drag from air i.e. loss of energy. But, we don't take that into account. Physics always has a habit of taking ideal cases. But if you want to consider the 'damping', it is not SHM. It is in that case, known as Damped Harmonic Motion.

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I'd prefer $y(t)=A\cos(\omega t + \phi )$ –  Bernhard Mar 13 '13 at 13:49
@Bernhard From the physics point of view, I would prefer the same, but I wrote the general form of the simple harmonic function. –  Cheeku Mar 13 '13 at 13:51