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

Options

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

Answer

C

Explanation

In series `k =k_(1)k_(2)//k_(1) + k_(2) = k^(2)//2k = k//2`. In parallel `k = k_(1) + k_(2) = 2k, n_(1) = (1//2pi) sqrt(k//2m)`
`n_(2) = (1//2pi) sqrt((2k//m)), n_(1) : n_(2) = 1: 2`