A spring has a certain mass suspended from it and period for vertical

1.	A spring has a certain mass suspended from it and period for vertical oscillation 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..
Answer» Answer: Given: Initial time PERIOD = T Spring is cut into 2 pieces and again suspended from one half To find: New time period Calculation: Let the initial Spring CONSTANT be K and FINAL spring constant be k2 . Since it is cut, we can say that : $= > k \times l = (k2) \times \dfrac{l}{2}$ $= > k = \dfrac{(k2)}{2}$ $= > k2 = 2k$ Initial time period = T $= > T = 2\pi \sqrt{ \dfrac{m}{k} }$ Putting new constant for spring : $T2 = 2\pi \sqrt{ \dfrac{m}{(k2)} }$ $= > T2 = 2\pi \sqrt{ \dfrac{m}{(2k)} }$ $= > T2 = \dfrac{1}{ \sqrt{2} } \bigg(2\pi \sqrt{ \dfrac{m}{k} } \bigg)$ $= > T2 = \dfrac{T}{ \sqrt{2} }$ So final answer : $\boxed{ \blue{ \huge{ \bold{ T2 = \dfrac{T}{ \sqrt{2} } }}}}$