Question

If the differential equation for a simple harmonic motion is $\frac{d^{2}y}{d{t}^2}+2y=0$, the time period of the motion is

• A. $\pi \sqrt{2}s$
• B. $\frac{\sqrt{2}}{\pi }s$
• C. $\frac{\pi }{\sqrt{2}}s$
• D. $2\pi s$
• E. $\frac{\sqrt{\pi }}{2}s$

Answer 1

The correct option is A $\pi \sqrt{2}s$

Given,
$\frac{d^{2}y}{d{t}^2}+2y=0$ ....(i)
But, we know that
$\frac{d^{2}y}{d{t}^2}+{\omega }^{2}y=0$ ....(ii)
Comparing both equation, we get
${\omega }^2=2$
$\Rightarrow \omega =\sqrt{2}$
The periodic time
$T=\frac{2\pi }{\omega }=\frac{2\pi }{\sqrt{2}}$
$T=\sqrt{2}\pi =\pi \sqrt{2}s$