In figure `S_(1)` and`S_(1)` are identical springs. The oscillation frequency of the mass `m` is `f`. if one spring is removed, the frequency will become

Options

A. `upsilon`
B. `2upsilon`
C. `sqrt(2)upsilon`
D. `(upsilon)/(sqrt(2))`

Answer

C

Explanation

The frequency of oscillation `(upsilon)` when mass is connected in between the two identicl springs is
`upsilon=(1)/(2pi)sqrt((2k)/(m))" " ...(i)`
The frequency of oscillation `(upsilon.)` when on of the springs is removed is `upsilon.=(1)/(2pi)sqrt((k)/(m))" "...(ii)`
Dividing (ii) by (i), we get
`(upsilon.)/(upsilon)=((1)/(2pi)sqrt((k)/(m)))/((1)/(2pi)sqrt((2k)/(m)))=(1)/(sqrt(2))orupsilon.=(1)/(sqrt(2))upsilon`