A particle undergoes simple harmonic motion driven by the restoring force of a spring, with a time period of T . If the spring is cut into two equal parts and one part is employed to continue the simple harmonic motion, the new time period will

Step-by-step solution

The time period of a particle in simple harmonic motion attached to a spring of spring constant k is given by T = 2 m k . The spring constant of a spring is inversely proportional to its length, so k 1 l . When the spring is cut into two equal parts, the length of each part becomes l' = l 2 . The new spring constant for one part is k' = 2k . The new time period T' is given by T' = 2 m k' = 2 m 2k . Substituting the initial time period, we get T' = T 2 .