A helical spring of stiffness (k) is cut into two halves and a mass (m) is connected

Question:

A helical spring of stiffness $k$ is cut into two halves and a mass $m$ is connected to the two halves as shown in Fig. 2.81(a). The natural time period of this system is found to be $0.5 \mathrm{~s}$. 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 Fig. 2.81(b), what would be the natural period of the system?

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