Q3 (a) Figure Q3(a) shows a rotational mechanical system with one (1) gear reduction unit installed on both shaft. Model the system and find the transfer function, G(s) = 02(s)/T₁(s) for the system. Assume the system with lossless gears. (10 marks) (b) Figure Q3(b) shows a translational mechanical system used in production control system. i. ii. Draw the free body diagram of the system. (2 marks) Using Newton's law of motion, write an appropriate equation of motion representing the system. (2 marks) iii. Transform the equation obtained in Q3(b)ii. into s-domain using the Laplace transform with the assumption of zero initial condition. (2 marks) iv. Sketch the block diagram of the system. (4 marks) T₁(t) 8₁(t) N₁ J₁ 8₁() K₂ www J₂ N₂ C2 T₁(t) HAMNAR O At HM Figure Q3(a) B₁ M₁₂ * K1 K₁₂ www Force, F B₁₂ Figure Q3(b) M2