The frequency of oscillations of a mass m suspended by spring of `v_(1)`. If the length of the spring is cut to one-third, the same mass oscillates with frequency `v_(2)`. Determing the value of `v_(2)//v_(1)`

Explanation

Let k be the spring constant of full spring. Then
`v_(1)=(1)/(2pi)sqrt((k)/(m))` …(i)
When the spring is cut to one-third of its length, its spring constant `k^(')=3k`. Now
`v_(2)=(1)/(2pi)sqrt((k^('))/(m))=(1)/(2pi)sqrt((3k)/(m)):. (v_(2))/(v_(1))=sqrt(3)`