The frequency of vertical oscillations of the three spring-mass system, shown in figure, is

Options

A. `(1)/(2pi)sqrt((3k)/(2m))`
B. `(1)/(2pi)sqrt((2k)/(3m))`
C. `(1)/(2pi)sqrt((2k)/(m))`
D. `(1)/(2pi)sqrt((k)/(3m))`

Answer

B

Explanation

`k_(eq)=((k+k)k)/((k+k)+k)=2k//3`
`T=2pisqrt((m)/(k_(eq)))=2pisqrt((m)/(2k//3))=2pisqrt((3m)/(2k))`
`f=1/T=(1)/(2pi)sqrt((2k)/(3m))`