What will be the period of the displacement body of mass `m`?

Options

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

Answer

C

Explanation

Equivalent force constant of three spring
`k_(eq) = (k_(1)k_(2))/(k_(1) + k_(2)) = (k xx 2k)/(3k) = (2k)/(3)`
`T = 2pi sqrt((m)/(k_(eq))) = 2pi sqrt((m)/(2k//3))`
`rArr T = 2pi sqrt((3m)/(2k))`