A particle executes simple harmonic motion with a time period of 16 s along the x - axis. At time t = 2 s , the particle crosses the mean position while at t = 4 s , the velocity of the particle is + 4 m s - 1 . The amplitude of motion (in m ) is

Step-by-step solution

The general equation of SHM is x = A sin ω t + ϕ , here ω = 2 π 16 = π 8   rad   s - 1 At t = 2   s , the particle is at the mean position. Hence, 0 = A sin π 8 × 2 + ϕ ⇒ ϕ = - π 4 So the equation of SHM will become x = A sin π 8 t - π 4 v = π A 8 cos π 8 t - π 4 At t =   4   s 4 = π A 8 cos π 8 × 4 - π 4 4 = π A 8 cos π 4 ⇒ A = 32 2 π   m