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 of mass 

D) Half of mass

Answer 1

A) Reduce the mass to one fourth

Explanations:

The frequency of spring oscillator is

\(v=\frac{1}{2\pi}\sqrt\frac{k}{m}\)

\(\implies v\propto \sqrt\frac{1}{m}\)

Hence \(\frac {v_1}{v_2}=\sqrt\frac{m_2}{m_1}\)

or \(\frac{m_2}{m_1}=(\frac{v_1}{v_2})^2=(\frac{v}{2v})^2=\frac{1}{4}\)

\(m_2=\frac{m_1}{4}\)