Q. A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n.$ What will be the frequency of the system if a mass $4\ m$ is suspended from the same spring
A) $n/4$
B) $4n$
C) $n/2$
D) $2n$
Explanation
(c) $n = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \Rightarrow n \propto \frac{1}{\sqrt{m}} \Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{m_{2}}{m_{1}}}$
$\Rightarrow \frac{n}{n_{2}} = \sqrt{\frac{4m}{m}} \Rightarrow n_{2} = \frac{n}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.