The displacement of the particle is given by:

\(x  =A \sin (-2 \omega t)+B \sin ^2 \omega t\)

\(=-A \sin 2 \omega t+\frac{B}{2}(1-\cos 2 \omega t)\)

\(=-\left(A \sin 2 \omega t+\frac{B}{2} \cos 2 \omega t\right)+\frac{B}{2}\)

This motion represents SHM with an amplitude: \(\sqrt{A^2+\frac{B^2}{4}}\), and mean position \(\frac{B}{2}\)