Physics - SHM Question with Solution | TestHub

The differential equation of simple harmonic motion is $$\frac{d^{2}y}{d{t}^2}+2y=0\text{ or }\frac{d^{2}y}{d{t}^2}=-2y......(i)$$ Standard equation of simple harmonic motion is $$\frac{d^{2}y}{d{t}^2}=-{\omega }^{2}y......(ii)$$ Comparing eq. (i) and (ii), ${\omega }^2=2$ or $\omega =\sqrt{2}$ As we know, $\omega =\frac{2\pi }{T}$ $\therefore$ Time period, $T=\frac{2\pi }{\omega }=\frac{2\pi }{\sqrt{2}}=\pi \sqrt{2}\sec$