Question

In the fig. $S1$ and $S2$ are identical springs. The oscillation frequency of 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. $f/\sqrt{2}$

Answer 1

Answer: (C), (D)

The correct options are
C $f\times \sqrt{2}$
D $f/\sqrt{2}$

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
$f^{\prime }=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$ .....(ii)
From equation (i) and (ii), $\frac{f}{f^{\prime }}=\sqrt{2}\Rightarrow f^{\prime }=\frac{f}{\sqrt{2}}$