Question

A spring is vibrating with frequency under same mass. If it is cut into two equal pieces and same mass is suspended then the new frequency will be

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

Answer 1

The correct option is A $n\sqrt{2}$

For a vibrating spring $n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
Now spring is cut into two pieces, so new spring constant $K^{{}^{\prime }}=2k$
$n^{{}^{\prime }}=\frac{1}{2\pi }\sqrt{\frac{2k}{m}}=n\sqrt{2}$