A particle's motion is described by the equation x = A ω t + B ω t...

Given equation of motion is $x = A \sin\omega t + B \cos\omega t$.

Multiplying and dividing the right side by $\sqrt{A^2 + B^2}$:

x = \sqrt{A^2 + B^2} \left(\dfrac{A}{\sqrt{A^2 + B^2}} \sin\omega$t +$\dfrac{B}{\sqrt{A^2 + B^2}} \cos\omegat \right)

Let $\cos\phi =$\dfrac{A}{\sqrt{A^2 + B^2}} and $\sin\phi =$\dfrac{B}{\sqrt{A^2 + B^2}}.

Substituting these values, we get:

$x =$\sqrt{A^2 + B^2} (\sin\omega$t \cos\phi + \cos\omega t \sin\phi)$

$x =$\sqrt{A^2 + B^2} \sin(\omega$t + \phi)<br><br>This represents simple harmonic motion with an amplitude of \sqrt{A^2 + B^2}.$