A body of mass `m` is suspended from three springs as shown in figure. If mass `m` is displaced slightly then time period of oscillation is

Options

A. `2pi sqrt((m)/(3K))`
B. `2pi sqrt((3m)/(2K))`
C. `2pi sqrt((2m)/(3K))`
D. `2pi sqrt((3K)/(m))`

Answer

B

Explanation

`K_(1) = k, K_(2) = 2k`
Effective force constant
`K = (k_(1)k_(2))/(k_(1)+k_(2)) = (k xx 2k)/(k + 2k) = (2k)/(3)`
`T = 2pi sqrt((3m)/(2k))`