A particle moves along the Y-axis according to the equation $y=a+b \sin wt$. The motion is simple harmonic. The maximum acceleration of the particle has a magnitude of

The equation $y=a+b\sin \left(\omega t\right)$ suggests that the particle is executing Simple Harmonic Motion about B which is the mean position and the amplitude of oscillation of the SHM (about B) is equal to A.

Hence, maximum acceleration of particle $=b{\omega }^2$