For the arrangement shown in the figure, find the period of oscillation

When the block displaced down by x, the spring will stretch by x2  From the free body diagram of the pulley, kx2 =2T  or T=kx4The net restoring force on the block is T. Using the Second Law of motion, we get md2xdt2=-T=-kx4d2xdt2=-kx4m=ω2x ω=k4m      T=2π4mk