As shown in figure, a simple harmonic motion oscillator having identical four springs has time period.

In the given figure, the two springs above are in parallel with each other, giving an equivalent spring constant of k+k=2k. Similarly the two springs below are also connected in series with each other, and giving an equivalent spring constant of k+k=2k. These two springs are connected in series giving net spring constant for the system = (2k)(2k)/(2k+2k) = k. Hence the time period of the motion of system = 2π√m/k