Four massless spring whose force constant are `2k , 2k, k` and `2k` respectively are attached to a mass `M` kept on a frictions plate (as shown in figure) if the mass `M` is displaced in the horizontal direction then the frequency of oscillation of the system is

Options

A. `(1)/(2pi) sqrt((k)/(4M))`
B. `(1)/(2pi) sqrt((4k)/(M))`
C. `(1)/(2pi) sqrt((k)/(7M))`
D. `(1)/(2pi) sqrt((7k)/(M))`

Answer

B

Explanation

The spring on left side having spring constant of `2k` each are in saries equvalent constant is `(1)/(((1)/(2k) + (1)/(2k))) = k`. The two spring on right hand side of mass `M` are in parallel Their effective spring constant is `(k + 2k) = 3k`.
Equivalent spring constant of value `k` and `3k` are in parallel and their and their net value of spring constant of all the four spring is `k + 3k = 4k`
:. Frequency of mass is `n = (1)/(2pi) sqrt((4k)/(M))`.