friction - Can a simple pendulum be considered a simple harmonic oscillator?

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

Answer

$y(\theta) = A\sin \theta+ B \cos \theta$ 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.