A particle is executing SHM according to the equation x=Acos⁡ωt. Average speed of the particle during the interval 0≤t≤π6ω.

Average velocity v¯=∫0t dxdt⋅dtt=∫0t dxt=x(t)−x(0)t=A(cos⁡π/6−1)π/6ω=3Aωπ(3−2)Since particle does not change its direction in the given interval, average speed becomes |v¯|=3Aωπ(2−3)