Question

For the given experimental setup, the oscillation frequency of the mass is $f.S_1$ and $S_2$ are identical springs. One spring is now removed, then frequency will become.

• A. $2f$
• B. $\frac{f}{\sqrt{2}}$
• C. $\frac{f}{\sqrt{3}}$
• D. $\sqrt{2}f$

Answer 1

The correct option is B $\frac{f}{\sqrt{2}}$

Frequency $f=\frac{1}{2\pi }\sqrt{\frac{k_{eq}}{m}}$
$=\frac{1}{2\pi }\sqrt{\frac{2k}{m}}$
One spring is removed, then $k_{eq}=k$
$f^{\prime }=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
$\Rightarrow \frac{f}{f^{\prime }}=\sqrt{2}$
$\Rightarrow f^{\prime }=\frac{f}{\sqrt{2}}$