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DISCUSSION and HINTS

You need to break the problem into two parts: during impact and between post-impact and the maximum rotation angle of the bar. For the during impact portion, consider the following:

Step 1: FBDs
Draw a single free body diagram including the two pendulum masses, the bullet and the bar.

Step 2: Kinetics (linear impulse/momentum)
Is angular momentum for the system about point O conserved? If so, why? Energy is NOT conserved. Why?

Step 3: Kinematics
After impact, the velocity of the bullet is the same as the velocity of the lower pendulum mass. You need to relate the speeds of the two pendulum masses and the bullet to the angular speed of the bar using rigid body kinematics.

Step 4: Solve
From your equations solve for the velocities of the two pendulum masses and the bullet.

After impact, consider using conservation of energy for the system of the two pendulum masses and the bullet together.