A particle travels along the X-axis described by the equation x = A...

The given equation of motion is $x = A + B \sin\omega t$.

Rearranging the terms, we get $x - A = B \sin\omega t$.

This equation represents a simple harmonic motion about the mean position $x = A$.

The amplitude of the motion is the maximum displacement from the mean position.

Since the maximum value of $\sin\omega t$ is $1$, the maximum displacement from the mean position is $B$.

Therefore, the amplitude of the simple harmonic motion is $B$.