Question

In the given diagram $S_{1}$ and $S_{2}$ are identical springs. The frequency of oscillation of the mass $m$ is $f$. If one of the springs is removed, then frequency will be

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

Answer 1

Answer: (D)

Effective spring constant, $k=2 k$
Frequency of oscillation, $f=\frac{1}{2 \pi} \sqrt{\frac{2 k}{m}}$
When one spring is removed, then spring factor $=k$
New frequency of oscillation will be constant
$f' =\frac{1}{2 \pi} \sqrt{\frac{k}{m}}$
$=\frac{f}{\sqrt{2}}$