A body is suspended at the end of a spring hanging vertically and it oscillates with a time period of 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 vertically and it o

1.	A body is suspended at the end of a spring hanging vertically and it oscillates with a time period of 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= 2pisqrt((m)/(K))` ,……….(1) When the spring is CUT into two pieces the force constant of each piece is given by `k^(1) = 2k`………(2) `:.` Period of oscillation `T^(1)= 2pisqrt((m)/(k))` ..........(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`