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)`

Options

A. `2`
B. `sqrt(2)`
C. `4`
D. `sqrt(3)`

Answer

B

Explanation

The frequency of oscillations of mass m and force constant k is, `upsilon_(1)=(1)/(2pi)sqrt((k)/(m))`
When the spring is cut to one-half of its length, its force constant is doubled (2k).
then frequency of oscillation of mass m will be
`upsilon_(2)=(1)/(2pi)sqrt((2k)/(m))" "therefore(upsilon_(2))/(upsilon_(1))=sqrt(2)`