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