Explanation

(c) Displacement equation
$y = A\sin{\omega t - B\cos{\omega t}}$
Let $A = a\cos\theta\ \ \ \ \ \ \ \ \ \ \ and\ \ \ \ \ \ \ \ \ \ \ \ \ B = a\sin{\theta\ }$
So, $A^{2} + B^{2} = a^{2}$
$\Rightarrow \ \ \ \ \ \ \ \ \ a = \sqrt{A^{2} + B^{2}}$
Then$_{,}$ $y = a\cos\theta\sin{\omega t} - a\sin\theta\cos{\omega t}$
$y = a\sin{(\omega t - \theta)}$
which is the equation of simple harmonic oscillator
The amplitude of the oscillator
$= a = \sqrt{A^{2} + B^{2}}$