A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves as shown below Fig. 1-(a). The natural time period of this system is found to be 0.5 s. If an identical spring is cut so that one part is one-fourth and the other part three-fourths of the original length, and the mass m is connected to the two parts as shown in below Fig. 1-(b), what would be the natural period of the system?