A simple harmonic oscillator consists of a particle of mass $'m'$ and an ideal spring with spring constant $'k'$. The particle oscillates with a time period 'T'. The spring is cut into two equal parts. If one part oscillates with the same particle , the time period will be :

Question

$$\begin {array} {1 1} (a)\;2T & \quad (b)\;\sqrt 2 T \\ (c)\;T/{\sqrt 2} & \quad (d)\;\frac{T}{2} \end {array}$$