$y(\theta) = A\sin \theta+ B \cos \theta$ 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.
A body is said to be executing S.H.M. if it oscillates about a fixed mean position and the motion should be periodic i.e. body takes equal time to reach its mean position in several repetetions......(All S.H.Ms are periodic in nature but all periodic motions are not simple harmonic)......
protected by Qmechanic♦ May 5 '13 at 17:30
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