Question

A mass $m$ is suspended from a spring. Its frequency of oscillation is $f$. The spring is cut into equal halves and the same mass is suspended from one of the two pieces of the spring. The frequency of oscillation is the mass will be

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

Answer 1

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

Let initial spring constant be k. Then, we can say,
$f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
After the spring is cut in two halves, spring constant becomes 2k. Then,
$f_2=\frac{1}{2\pi }\sqrt{\frac{2k}{m}}=\sqrt{2}f$. Option A is thus correct.