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
AIPMT 1998, Medium
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(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}}$
$4\Rightarrow {n_2} = \frac{n}{2}$
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