Question

A mass of 1 kg attached to the bottom of a spring has a certain frequency of vibration. The following mass has to be added to it in order to reduce the frequency by half :

• A. 1 kg
• B. 2 kg
• C. 3 kg
• D. 4 kg

Answer 1

The correct option is C 3 kg

For a spring mass system the angular frequency is given by :

$\omega =\surd \left(k/m\right)..........\left(1\right)$

let $m^{\prime }$ be the mass of the system after adding weight, then,

${\omega }^{\prime }=\surd \left(k/m^{\prime }\right)...................eq2$

dividing eqn 1 by eqn2 we get

$\omega /{\omega }^{\prime }=\surd \left(m^{\prime }/m\right)$

since the system frequency becomes half, so $\omega /{\omega }^{\prime }=2$

also given mass, $m=1kg$

Hence putting these value in the above equation we get,

$2=\surd \left(m^{\prime }/1\right)$

$=>m^{\prime }=4kg$

so mass that needs to be added to the system to make whole mass $4kg$

$=4-1$

$=3kg.$

Hence, the option $C$ is the correct answer.