Time period of oscillation of a mass suspended from a spring is T . If the spring is cut into four equal parts and the same mass is suspended from one of the parts, the fractional change in time period is

Step-by-step solution

The time period of a mass m suspended from a spring of force constant k is given by T = 2 m k . When a spring of force constant k is cut into n equal parts, the force constant of each part becomes k' = nk . Here, n = 4 , so k' = 4k . The new time period T' for the same mass m suspended from one of the parts is T' = 2 m k' = 2 m 4k = 1 2 2 m k = T 2 . The fractional change in the time period is given by | T' - T T | = | T 2 - T T | = | - T 2 T | = 1 2 . Answer: 1 2