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

Answer

A

Explanation

Two springs on the LHS of mass M are in series and two springs on the RHS of mass M are in parallel. These combination of springs will be considered in parallel to mass M. Thus, the equivalent spring constant is `k_(eq)=(2kxx2k)/(2k+2k)+(k+k)=4k`
`therefore` Frequency, `upsilon=(1)/(2pi)sqrt((k_(eq))/(M))=(1)/(2pi)sqrt((4k)/(M))`