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

Step-by-step solution

The displacement of a mass in simple harmonic motion is given by x = 3 10⁻³ (2 t) meters. This matches the standard form x = A ( t) , where A = 3 10⁻³ m is the amplitude and = 2 rad/s is the angular frequency. Velocity is found by differentiating displacement: v = dx dt = -6 10⁻³ (2 t) m/s. Speed reaches its maximum when | (2 t)| = 1 , which occurs as the mass crosses the equilibrium position for the first time after starting at maximum positive displacement. The time of maximum speed corresponds to (2 t) = 0 . The