Question

$S_1$ and $S_2$ are two identical springs. The oscillation frequency is $f$ . If one spring is removed, frequency will be

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

Answer 1

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

The frequency of this case is given by, $f=\frac{1}{2\pi }\sqrt{\frac{2k}{M}}$

Where, $M=$ Mass of block,

$k=$ Spring constant

Now, if one spring is removed, the frequency of oscillation will be, $f^{\prime }=\frac{1}{2\pi }\sqrt{\frac{k}{M}}$

So, $\frac{f^{\prime }}{f}=\frac{\frac{1}{2\pi }\sqrt{\frac{k}{M}}}{\frac{1}{2\pi }\sqrt{\frac{2k}{M}}}=\frac{1}{\sqrt{2}}$

Or, $f^{\prime }=\frac{f}{\sqrt{2}}$