A body is suspended at the end of a spring hanging verticaly and it oscillates with a time periodof 1.414 s. The spring is then cut into two equal parts and the same body attached to one of the pieces is made to oscillate. What be the time period of oscillation?

A body is suspended at the end of a spring hanging verticaly and it os

1.	A body is suspended at the end of a spring hanging verticaly and it oscillates with a time periodof 1.414 s. The spring is then cut into two equal parts and the same body attached to one of the pieces is made to oscillate. What be the time period of oscillation?
Answer» Solution :The TIME period of oscillation of the SPRING -mass system is given by `T=2pi sqrt(m/k)`………1 When the spring is CUT two pieces the forces constant of each piece is gives by `k^(1)=2k`. ………..2 `:.` Period of oscillation `T^(1)=2pisqrt(m/(k^(1))`.................3 From 1 & 3 we get `T/(T^(1))=sqrt((k^(1))/k)` But `T=1.414s, T^(1)=?` `:.1.414/(T^(1))=sqrt((2k)/k)=sqrt(2):.T^(1)=1S`