Return to Answer

It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.

For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.

EDIT:

Even for a horizontal mass-spring system the displacement of the mass from its equilibrium position cannot be made too large, otherwise the simple-harmonic motion ceases to be valid.

It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.

For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.

EDIT:

Even for a horizontal mass-spring system the displacement of the mass from its equilibrium position cannot be made too large, otherwise the simple-harmonic motion ceases to be valid.

But whether considering a pendulum undergoing SHM or a mass-spring system the displacement from equilibrium position is $\propto$ to the negative of the acceleration towards the equilibrium point as these are in opposite directions which is the reason for the minus sign.

It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.

For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.

It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.

For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.

EDIT:

Even for a horizontal mass-spring system the displacement of the mass from its equilibrium position cannot be made too large, otherwise the simple-harmonic motion ceases to be valid.

It just means that the pendulum will only execute SHM with small angles for which the pendulum is displaced from equilibrium.

For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.

It just means that the pendulum will only execute SHM with small angles for which the pendulum subtends as it oscillates.

For larger angles the motion of the pendulum deviates from being simple harmonic; that's why the small angle approximation is required in the derivation.