Two identical spring of constant K are connected in series and parallel as shown in figure. A mass is suspended from them. The ratio of their frequencies of vertical oscillations will be

Options

A. `2:1`
B. `1:1`
C. `1:2`
D. `4:1`

Answer

A

Explanation

(A) `K_(eq)=(k k)/(2k)=(k)/(2)`
`T_(1)=2pisqrt((m)/(k//2)) implies (1)/(f_(1))=2pisqrt((k)/(2m))`
(B) `K_(eq)=2k`
`T_(2)=2pisqrt((m)/(2k))implies (1)/(f_(2)) =2pisqrt((2k)/(m))`
`(f_(1))/(f_(2))=(2)/(1)`.