Four mass less spring whose force constant are `2k , 2k, k` and `2k` respectively are attached to a mass `M` kept on a friction less 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)/(4M))`
C. `(1)/(2pi)sqrt((k)/(7M))`
D. `(1)/(2pi)sqrt((7k)/(M))`

Answer

B

Explanation

Two springs on the `L.H.S` of mass `M` are in series and two springs on the `R.H.S.` of mass `M` are in parallel. These combination of springs will be considered in parallel to mass `M` . Thus effective
spring constant, `K=(2kxx2k)/(2k+2k)+(k+2k)=4k`
Inertia factor `=` mass attached to the spring `=M`
`:. ` Frequecny `v=(1)/(2pi)sqrt((spri ng fact o r)/(i n ertia fact o r))`
`=(1)/(2pi)sqrt((4k)/(M))`