The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is

As x given in the question satisfies the simple harmonic motion equation

the above equation in question is a simple harmonic motion.

And can be represented as

Where , δ is the phase difference and .

And ,

In which can also be represented as,

δ can be written as

And becomes

Hence, amplitude becomes.