The 4-lb uniform slender rod AB, the 8-lb uniform slender rod BF, and the 4-lb uniform thin

Question:

The 4-lb uniform slender rod AB, the 8-lb uniform slender rod BF, and the 4-lb uniform thin sleeve CE are connected as shown and move without friction in a vertical plane. The motion of the linkage is controlled by the couple M applied to rod AB. Knowing that at the instant shown the angular velocity of rod AB is 30 rad/s and the angular acceleration of rod AB is 96 rad/s2 clockwise, determine

(a) The magnitude of the couple M,

(b) The reaction at point D.