Question

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 $4m$ is suspended from the same spring

• A. $n/4$
• B. $4n$
• C. $n/2$
• D. $2n$

Answer 1

Answer: (C)

$n/2$

$n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\Rightarrow n\propto \frac{1}{\sqrt{m}}\Rightarrow \frac{n_1}{n_2}=\sqrt{\frac{m_2}{m_1}}$
$\Rightarrow \frac{n_1}{n_2}=\sqrt{\frac{4m}{m}}\Rightarrow n_2=\frac{n}{2}$