Question

The equation of motion of a particle of mass $1g$ is $\frac{d^{2}x}{d{t}^2}+{\pi }^{2}x=0$, where $x$ is displacement $\left(inm\right)$ from mean position. The frequency of oscillation is $\left(inHz\right)$:

• A. $\frac{1}{2}$
• B. $2$
• C. $5\sqrt{10}$
• D. $\frac{1}{5\sqrt{10}}$

Answer 1

The correct option is A $\frac{1}{2}$

$\frac{d^{2}x}{d{t}^2}=-{\pi }^{2}x$
Comparing with $\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}x$
We have,
$\omega =\pi$
$\therefore$ $2\pi f=\pi$
$f=\frac{1}{2}$ Hz