Question

A mass of 1 kg attached to the bottom of a spring has certain frequency of vibration. What mass is to be added in order to reduce the frequency by half?
(a) 1 kg
(b) 2 kg
(c) 3 kg
(d) 4 kg

Answer 1

3 kg of mass option(c) needs to be added to make the frequency half.

EXPLANATION :

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

ω = √(k/m)..........eq1

let m' be the mass of the system after adding weight, then,

ω' = √(k/m')...................eq2

dividing eqn 1 by eqn2 we get

ω/ω' = √(m'/m)

since the system frequency becomes half, so ω/ω' = 2

also given mass, m = 1 kg

Hence putting these value in the above equation we get,

2 = √(m'/1)

=> m' = 4 kg

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

= 4 - 1

= 3 kg.