Question

A block of mass m, when attached to a uniform ideal spring with force constant k and free length L executes SHM. The spring is then cut in two pieces, one with free length nL and other with free length (1-n)L. The block is also divided in the same fraction. The smaller part of the block attached to longer part of the spring executes SHM with frequency $f_1$. The bigger part of the block attached to smaller part of the spring executes SHM with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is

• A. 1
• B.
• C.
• D.

Answer 1

The correct option is A

1

$T=2\pi \sqrt{\frac{m}{k}}=\frac{1}{f}$;

$T_1=2\pi \sqrt{\frac{m(1-n)}{\frac{k}{n}}}$ and $T_2=2\pi \sqrt{\frac{nm}{\frac{k}{(1-n)}}}$

$\frac{f_1}{f_2}=\frac{T_1}{T_2}=\sqrt{\frac{nm(1-n)}{k}}\sqrt{\frac{k}{nm(1-n)}}=1$