Question

The equation of motion of a particle of mass $1\text{g}$ is $\frac{d^{2}x}{d{t}^2}+{\pi }^{2}x=0$, where $x$ is displacement (in $\text{m}$) from mean position. The frequency (in $\text{Hz}$) of oscillation is

• A. $0.5$
• B. $0.7$
• C. $0.8$
• D. $0.3$

Answer 1

The correct option is A $0.5$

Given, equation of motion,
$\frac{d^{2}x}{d{t}^2}+{\pi }^{2}x=0$
On comparing with standard equation of simple harmonic motion,
$\frac{d^{2}x}{d{t}^2}+{\omega }_o^{2}x=0$,
We get, ${\omega }_o=\pi$
So, $f=\frac{{\omega }_o}{2\pi }=\frac{\pi }{2\pi }=\frac{1}{2}=0.5\text{Hz}$