A mass attached to a spring performs S.H.M. whose displacement is x = 3 10⁻³ 2 t m. The time taken to obtain maximum speed for the first time is (in s)

Step-by-step solution

The displacement of the particle is given by x = 3 10⁻³ (2 t) . The velocity of the particle is v = dx dt = -6 10⁻³ (2 t) . The speed is maximum when the magnitude of velocity is maximum, which occurs when | (2 t)| = 1 . For the first time, this happens when 2 t = 2 . t = 1 4 s. Alternatively, the particle starts from the extreme position at t = 0 . The speed is maximum at the mean position, which it reaches for the first time at t = T 4 . Comparing with x = A ( t) , we get = 2 . Time period T = 2 = 2 2 = 1 s. Time