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 the figure. If the mass M is displaced in the horizontal direction, then the frequency of the system is?

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 combinations of springs will be considered in parallel to mass M. Thus effective spring constant, K = (2k × 2k)/(2k + 2k) + (k + 2k) = 4k/4 + 3k = k + 3k = 4k
∴ Frequency v = 1/(2π)√(K/M) = 1/(2π)√(4k/M).