Question

To make the frequency double of a spring oscillator, we have to

• A. reduce the mass to one-fourth
• B. quadruple the mass
• C. double the mass
• D. half the mass

Answer 1

Answer: (A)

reduce the mass to one-fourth

Answer 2

The frequency of spring oscillator is $v=\frac{1}{2 \pi} \sqrt{\left(\frac{k}{m}\right)}$ $\Rightarrow v \propto \sqrt{\left(\frac{1}{m}\right)}$ Hence, $\frac{v_{1}}{v_{2}}=\sqrt{\left(\frac{m_{2}}{m_{1}}\right)}$ or $\frac{m_{2}}{m_{1}}=\left(\frac{v_{1}}{v_{2}}\right)^{2}$ $=\left(\frac{v}{2 v}\right)=\frac{1}{4}$ $\therefore {m}_{2}=\frac{m_{1}}{4}$