Question

A spring of stiffness constant `k` and natural length `l` is cut into two parts of length `3l//4 and l//4`, respectively, and an arrangement is made as shown in figure . If the mass is slightly displaced , find the time period of oscillation.

Answer 1

The stiffness of a spring is inversely proportional to its length . Therefore the stiffness of each part is
`k_(1) = (4)/(3) k` and `k_(2) = 4 k`
Time period `T = 2 pi sqrt((m)/(k_(1) + k_(2)))`
`= 2 pi sqrt ((3m)/(16 k)) = (pi)/(2) sqrt((3 m)/(k))`