Physics - SHM Question with Solution | TestHub

$y=\sin \omega t-\cos \omega t$ $$\begin{array}{rl}\frac{dy}{dt}& =\omega \cos \omega t+\omega \sin \omega t\\ \frac{dy}{dt}& =-{\omega }^2\sin \omega t+{\omega }^2\cos \omega t\\ & =-{\omega }^2(\sin \omega t-\cos \omega t).\\ a& =-{\omega }^{2}y.\therefore a\propto -y.\end{array}$$ which is the condition of simple harmonic motion.