Question

A body of mass m is suspended from vertical spring of length l executes shm with time period t .find the time period if the length of the string is made half?? ​

Answer 1

Let m be the mass , l be the initial length and t is the initial time period

Initially,

t = 2π√(k/m) [k is the spring constant , k= F/l]

t= 2π√(F/ml)

When length is halved , l' = l/2

t' - final time period

t' = 2π√(F/ml')

t' = 2π√(2F/ml)

t'=√2 t