In the figure, `S_(1) and S_(2)` are identical springs. The oscillation frequency of the mass m is f. If one spring is removed, the frequency will become

Options

A. f
B. 2f
C. sqrt(2)f
D. (1)/(sqrt(2))f

Answer

D

Explanation

For the given figure,
`f = (1)/(2pi) sqrt((k_(eq))/(m))=(1)/(2pi) sqrt((2k)/(m))" "...(i)`
If one spring is removed, then `k_(eq) = k` and
`f' = (1)/(2pi) sqrt((k)/(m))" "...(ii)`
From Eqs. (i) and (ii), we get `(f)/(f')=sqrt(2) rArr f'=(1)/(sqrt(2))f`