Question

A uniform spring has certain mass suspended from it and it's period

Answer 1

your question is incomplete.A complete question is ------> A spring has a certain mass suspended from it and its period for vertical position is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves.The period of vertical oscillation is now.

time period of oscillation of spring mass system is given by, T=$2\pi\sqrt{\frac{m}{k}}$
where m is mass of body suspended in spring. k is spring constant.

here it is clear that, spring constant is inversely proportional to spring constant.

when we cut spring into two equal halves then, spring constant of each half will be two times of initial value . e.g., k' = 2k

hence, new time period , T' = $2\pi\sqrt{\frac{m}{k'}}$

$T'=2\pi\sqrt{\frac{m}{2k}}$

or, T' = $\frac{1}{\sqrt{2}}2\pi\sqrt{\frac{m}{k}}$

hence, T' = T/√2