In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
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(d) For the given figure $f = \frac{1}{{2\pi }}\sqrt {\frac{{{k_{eq}}}}{m}} = \frac{1}{{2\pi }}\sqrt {\frac{{2k}}{m}} $…..(i)
If one spring is removed, then $k_eq = k$ and
$f' = \frac{1}{{2\pi }}\sqrt {\frac{k}{m}} $ ….(ii)
From equation (i) and (ii),
If one spring is removed, then $k_eq = k$ and
$f' = \frac{1}{{2\pi }}\sqrt {\frac{k}{m}} $ ….(ii)
From equation (i) and (ii),
$\frac{f}{{f'}} = \sqrt 2 $
==> $f' = \frac{f}{{\sqrt 2 }}$
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