The design of the rotating arm OA of a control mechanism requires that it rotate about t...

The design of the rotating arm OA of a control mechanism requires that it rotate about the vertical Z-axis at the constant rate Simultaneously, OA oscillates according to θ = θ₀ sin 4Ωt, where θ₀ = π/6 radians and t is in seconds measured from the time when . Determine the angular velocity ω and the angular acceleration α of OA for the instant (a) when t = 1/2 s and (b) when t = 1/8 s. The x-y reference axes rotate in the X-Y plane with the angular velocity Ω.