A particle moves on the X-axis according to the equation x=A+Bsinω t. The motion is simple harmonic with amplitude.
We are given x=A+B sinω t
We can see that the second term basically is the equation of an SHM with amplitude B. What's the first term doing there? Let's think about it. If it were just B sin ωt, it would be an SHM about the origin. Adding a constant to this entire thing would just shift the mean position from origin to x = A. Now the particle is doing SHM about x = A with an amplitude of B. Yes B! because amplitude is how far the particle goes from the mean position. The new means position is x = A but the particle's max displacement is still B from it!