Q. 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
A) $f$
B) $f \times 2$
C) $f \times \sqrt{2}$
D) $f/\sqrt{2}$
Explanation
(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
$f^{'} = \frac{1}{2\pi}\sqrt{\frac{k}{m}}\ \ \ \ \ \ \ \ \ldots(ii)$
From equation (i) and (ii),
$\frac{f}{f^{'}} = \sqrt{2} \Rightarrow f^{'} = \frac{f}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.