Question

A body of mass ${}^{\prime }{m}^{\prime }$ is hung from a long and light spring. The spring is stretched by $0.2m$. The period of the vibration of the mass when pulled down and released is :

• A. $\frac{2\pi }{7}s$
• B. $\frac{\pi }{7}s$
• C. $\frac{4\pi }{7}s$
• D. $7\pi s$

Answer 1

The correct option is A $\frac{2\pi }{7}s$

Given,

$g=9.8m/s^2$

$x=0.2m$

By hook's law,

$F=mg=-kx$

$\frac{k}{m}=\frac{9.8}{0.2}=49s^{-2}$ (taking only magnitude)

$\frac{m}{k}=\frac{1}{49}{s}^2$

The time period of the vibration of the mass when pulled down and released

$T=2\pi .\sqrt{\frac{m}{k}}$

$T=2\pi \sqrt{\frac{1}{49}}$

$T=\frac{2\pi }{7}s$

The correct option is A.