For a particle executing simple harmonic motion, the time period is equal to the minimum time interval between the particle attaining a specific velocity v . The value of v is

Step-by-step solution

The velocity of a particle executing simple harmonic motion is given by v = v_ max ( t) . The time period of the oscillation is T = 2 . We need to find the velocity v for which the minimum time interval between two consecutive instances of attaining this specific velocity is exactly T . If v = 0 , the particle is at the extreme positions. It attains zero velocity twice in one complete cycle (at the positive and negative extremes). The time interval between these instances is T 2 . If 0 If v = v_ max , the particle