A particle executes simple harmonic motion with a time period 0.6 ~s and amplitude 10 ~cm . Then the mean velocity of the particle over the time interval during which it travels a distance 5 ~cm starting from the equilibrium position.

Step-by-step solution

We have aligned & x=A t 5=10 t & 1 2 = t t= 6 = T 6 2 = T 12 aligned Then, V= dx dt = A t V = A t Now, aligned & V _ mean = ₀^ T / 12 ~A dt ₀^ T / 12 dt = A [ t ]₀^ T / 12 ~T / 12 & = A [ 1 2 -0 ] T 12 = 0.1 2 0.6 12 = 12 12 =1 ~m / s aligned