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

 

The two springs on left side having  spring constant of 2k each are in  series, equivalent constant is  
$\frac{1}{\left(\frac{1}{2\mathrm{k}}+\frac{1}{2\mathrm{k}}\right)}=\mathrm{k}.$ The two springs on right hand side of mass M are in parallel. Their effective spring constant is (K+2K)=3K.
           Equivalent spring constants of value k and  3k are in parallel and their net value of spring constant of all the four springs is k+3k=4k 

$\therefore \mathrm{Frequency}\mathrm{of}\mathrm{mass}\mathrm{is}\mathrm{n}=\frac{1}{2\mathrm{\pi }}\sqrt{\frac{4\mathrm{k}}{\mathrm{M}}}$