Simple harmonic motion~

Question

I am stuck in a question which says that: A particle moves on the X- axis according to equation $x=A+Bsin(\omega t)$. The motion is simple harmonic. Find the amplitude of SHM.

The answer of the above problem is "B".
My question is: how the above equation is simple harmonic? I do not know how to reach the answer. If there were two trig functions in the question then it would be easy to solve for the answer using vector addition method! The "A" in the equation is troubling me.

Answer 1

The constant $A$ is simply a vertical shift by $A$ units (this shift can be up--if $A>0$--or down if $A<0$).

By the way, the amplitude is $|B|$

Answer 2

Write

$$x(t)=A+B\cos\left(\frac\pi2-\omega t\right)$$

and then we easily see the amplitude indeed is $\;B\;$ . The $\;A\;$ is just translation.