Four massless springs whose force constants are `2k, 2k, k` and `2k` respectively are attached to a mass `M` kept on a fricaionless plane (as shown in figure). If the mass `M` is displaced in the horizontal directions, then the frequency of the system.

Options

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

Answer

B

Explanation

`k_(eq) = 2k + k + (2k xx 2k)/(2k + 2k) = 4k`
so, frequency, `f = (1)/(2pi) sqrt(K_(eq))/(M) = (1)/(2pi)sqrt(4K)/(M)`