Question

One-third of spring having force constant k is cut and mass m is suspended to it. If the frequency of oscillation of the original spring with the same mass is/then the frequency of oscillation in one-third of spring is

• A. $\frac{1}{\sqrt{3}}f$
• B. $\sqrt{3}f$
• C. $2f$
• D. $\frac{2}{\sqrt{3}}f$

Answer 1

Answer: (B)

$\sqrt{3}f$

Answer 2

: Force constant of full spring $=k,$ mass $=m$ $\therefore$ $T=2\pi \sqrt{\frac{m}{k}}$ or frequency $f=\frac{\sqrt{k}}{2\pi \sqrt{m}}$ Force constant for one-third spring $=3\text{ }k,$ mass $=m,$ $\therefore$ $f=\frac{\sqrt{3k}}{2\pi \sqrt{m}}$ $\therefore$ $f=\sqrt{3}f.$